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mathematics
calculus 10th edition

Questions and Answers of Calculus 10th Edition

In Exercises set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the y-axis. x y = 1/2 +3₁ +3, 1 ≤ x ≤ 5
A solid is generated by revolving the region bounded by y = √9 - x² and y = 0 about the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-third of
In Exercises find the volume generated by rotating the given region about the specified line.R3 about x = 0 1 0.5 R₁ R2 0.5 y=x² R3 + 1 y = x X
In Exercises the integral represents the volume of a solid of revolution. Identify (a) The plane region that is revolved(b) The axis of revolution fur y - y³/2 dy
In Exercises set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the y-axis. -22 4' y = 1 - 0≤x≤ 2
A solid is generated by revolving the region bounded by y = 1/2x² and y = 2 about the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-fourth of the
In Exercises the integral represents the volume of a solid of revolution. Identify (a) The plane region that is revolved(b) The axis of revolution 2π 0 (y + 2)√6-y dy
In Exercises find the volume generated by rotating the given region about the specified line.R₂ about y = 0 1 0.5 R₁ R2 0.5 y=x² R3 + 1 y = x X
In Exercises find the volume generated by rotating the given region about the specified line.R2 about y = 1 1 0.5 R₁ R2 0.5 y=x² R3 + 1 y = x X
In Exercises set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the y-axis. y=9-x² -4-2 y y=9-x² 2 4 X
In Exercises set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the y-axis. y = 3√x + 2 4 2 1 + -8-6-4-2 + |y= √√x+2] 2 4 6 8
In Exercises find the volume generated by rotating the given region about the specified line.R₁ about x = 0 1 0.5 R₁ R2 0.5 y=x² R3 + 1 y = x X
In Exercises the integral represents the volume of a solid of revolution. Identify (a) The plane region that is revolved(b) The axis of revolution ₁² x 2π Jo x dx
In Exercises find the volume generated by rotating the given region about the specified line. R₁ about x = 1 1 0.5 R₁ R2 0.5 y=x² R3 + 1 y = x X
In Exercises set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis. y = √√√9-x²₂ -2 ≤x≤ 2
The region in the figure is revolved about the indicated axes and line. Order the volumes of the resulting solids from least to greatest. Explain your reasoning.(a) x-axis(b) y-axis(c) x = 4
In Exercises use the integration capabilities of a graphing utility to approximate the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y
In Exercises set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis. y = 3x, 0≤x≤ 3
In Exercises set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis. || 6 - 2x² 1 ≤ x ≤ 2
In Exercises give a geometric argument that explains why the integrals have equal values. - So [16 (2y)²] dy = 2π 27 (² x (2) dx -
In Exercises use the integration capabilities of a graphing utility to approximate the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y
In Exercises give a geometric argument that explains why the integrals have equal values. 5 + S³ (x- 77 (x - 1) dx 1) dx = 2 277 ² M 2π 2π y[5 (y2 + 1)] dy -
In Exercises use the integration capabilities of a graphing utility to approximate the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y
In Exercises set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis. y = 2 x y - 6 4 2 -2 -4 6 - -6 y = 2x 2 4 6 - x 6 8
Consider the plane region bounded by the graphs ofwhere k > 0 and b > 0. What are the heights and radii of the cylinders generated when this region is revolved about(a) The x-axis (b) The
In Exercises use the integration capabilities of a graphing utility to approximate the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y
In Exercises set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis. |y= x³ 10- 8 2 + -4 -6 -8 -10- 3 X
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify your results using the integration capabilities of a
Find the arc length from (-3, 4) clockwise to (4, 3) along the circle x² + y² = 25. Show that the result is one-fourth the circumference of the circle.
Consider a solid that is generated by revolving a plane region about the -axis. Describe the position of a representative rectangle when using (a) The shell method (b) The disk method to
In Exercises(a) use a graphing utility to graph the plane region bounded by the graphs of the equations(b) use the integration capabilities of the graphing utility to approximate the volume of the
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify your results using the integration capabilities of a
In Exercises(a) use a graphing utility to graph the plane region bounded by the graphs of the equations(b) use the integration capabilities of the graphing utility to approximate the volume of the
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify your results using the integration capabilities of a
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify your results using the integration capabilities of a
Astroid Find the total length of the graph of the astroid x2/3 + y2/3 = 4. -6 8 2 -2 -6 -8 y x2/3 + y2/3=4 2 68 X
A barn is 100 feet long and 40 feet wide (see figure). A cross section of the roof is the inverted catenary y = 31 - 10(ex/20+ e-x/20). Find the number of square feetof roofing on the barn.
In Exercises(a) use a graphing utility to graph the plane region bounded by the graphs of the equations(b) use the integration capabilities of the graphing utility to approximate the volume of the
Find the arc length from (0, 3) clockwise to (2, √5) along the circle x² + y² = 9.
In Exercises(a) use a graphing utility to graph the plane region bounded by the graphs of the equations(b) use the integration capabilities of the graphing utility to approximate the volume of the
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. y=9x², y = 0, x = 2, x = 3
In Exercises use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines.(a) The x-axis(b)
Electrical wires suspended between two towers form a catenary (see figure) modeled by the equationwhere x and are measured in meters. The towers are 40 meters apart. Find the length of the suspended
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = √√x₂ y = − 1²/x +4₁ x=0, x=8
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. 0= x ¹0 = ²(x - 2)ε = ^
In Exercises use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines.(a) The x-axis(b)
In Exercises use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines.(a) The x-axis(b)
In Exercises approximate the arc length of the graph of the function over the interval [0, 4] in four ways. (a) Use the Distance Formula to find the distance between the endpoints of the
In Exercises approximate the arc length of the graph of the function over the interval [0, 4] in four ways. (a) Use the Distance Formula to find the distancebetween the endpoints of the
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = x² + 1, y = -x² + 2x + 5, x = 0, x = 3
In Exercises determine which value best approximates the length of the arc represented by the integral. (Make your selection on the basis of a sketch of the arc, not by performing any
In Exercises use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines.(a) The
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = ex/4, y = 0, x = 0, x = 6
In Exercises decide whether it is more convenient to use the disk method or the shell method to find the volume of the solid of revolution. Explain your reasoning. (Do not find the volume.) y = 4-
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = 2 x + 1' y = 0, x = 0, x = 6
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = e, y = 0, x = 0, y = 1
In Exercises decide whether it is more convenient to use the disk method or the shell method to find the volume of the solid of revolution. Explain your reasoning. (Do not find the volume.) (y-2)² =
In Exercises (a) Sketch the graph of the function, highlighting the part indicated by the given interval(b) Find a definite integral that represents the arc length of the curve over the
In Exercises use the shell method to find the volume of the solid generated by revolving the plane region about the given line. y 3x³, y = 6x x², about the line x = 3
In Exercises (a) Sketch the graph of the function, highlighting the part indicated by the given interval(b) Find a definite integral that represents the arc length of the curve over the
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. 1 y = 0, x= 1, x = 3
In Exercises use the shell method to find the volume of the solid generated by revolving the plane region about the given line. y = x², y = 4x - x², about the line x = 4
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = x² + 1 -2 -1 4 3 2 1 y 2
In Exercises (a) Sketch the graph of the function, highlighting the part indicated by the given interval(b) Find a definite integral that represents the arc length of the curve over the
In Exercises use the shell method to find the volume of the solid generated by revolving the plane region about the given line. y = √√x, y = 0, x = 4, about the line x = 6
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y=x√4x², y = 0
In Exercises use the shell method to find the volume of the solid generated by revolving the plane region about the given line. y = 2x - x², y = 0, about the line x = 4
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y 1 √x+1² y = 0, x=0, x = 4
In Exercises (a) Sketch the graph of the function, highlighting the part indicated by the given interval(b) Find a definite integral that represents the arc length of the curve over the
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = √√√x + 2, y = x, y = 0
In Exercises (a) Sketch the graph of the function, highlighting the part indicated by the given interval(b) Find a definite integral that represents the arc length of the curve over the
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = x y 2 1 수 1 2 X
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. x + y = 4, y = x, y = 0
In Exercises (a) Sketch the graph of the function, highlighting the part indicated by the given interval(b) Find a definite integral that represents the arc length of the curve over the
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = 4x², x = 0, y = 4
In Exercises (a) Sketch the graph of the function, highlighting the part indicated by the given interval(b) Find a definite integral that represents the arc length of the curve over the
In Exercises (a) Sketch the graph of the function, highlighting the part indicated by the given interval(b) Find a definite integral that represents the arc length of the curve over the
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 5. xy = 3, y = 1, y = 4, x = 5
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. x + y =
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = x³, x = 0, y = 8
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. || 1 | | نات - 34 2 - - + +
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 5. x = y², x = 4
In Exercises (a) Sketch the graph of the function, highlighting the part indicated by the given interval(b) Find a definite integral that represents the arc length of the curve over the
In Exercises (a) Sketch the graph of the function, highlighting the part indicated by the given interval(b) Find a definite integral that represents the arc length of the curve over the
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 4. y 3 1 + x² y = 0, x = 0, x = 3
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 4. y = sec x, y = 0, 0≤x≤ 3
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 5. y = 3 - x, y = 0, y = 2, x = 0
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 5.y = x, y = 0, y = 4, x = 5
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = 1 - x 2 1 y -1 -2+ 4 X
In Exercises find the arc length of the graph of the function over the indicated interval. x = √y(y - 3), 1≤ y ≤4
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 4. y = ½ x³, y = 4₂ x = 0 4,
In Exercises find the arc length of the graph of the function over the indicated interval. = (y² + 2)³/2, 0≤ y ≤ 4 X =
In Exercises find the arc length of the graph of the function over the indicated interval. y = In ex + 1 ex 1 - [In 2, In 3]
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = sin x X 1, x > 0 " x = 0 y = 0,
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. 1 y e-x²/2, y = 0, x= 0, х = 1 2 п
In Exercises find the arc length of the graph of the function over the indicated interval. y = (ex + e*), [0, 2]
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = √√x - 2, y = 0, x = 4
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 4.y = x, y = 3, x = 0
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = -x² + 1, y = 0
In Exercises find the arc length of the graph of the function over the indicated interval. y = In(cos x), 0,77 3

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