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mathematics
calculus 10th edition

Questions and Answers of Calculus 10th Edition

In Exercises find the indefinite integral. (5 + 4x²)² dx
In Exercises find the indefinite integral. 3x x + 4 dx
In Exercises find the indefinite integral. 2 2 [ x ( 3 + ² ) ² α dx
In Exercises find the indefinite integral. x cos 27x² dx
In Exercises find the indefinite integral. 15 sin x COS X dx
In Exercises find the indefinite integral. S csc² xe cotx dx
In Exercises find the indefinite integral. csc 7x cot 7x dx
In Exercises find the indefinite integral. 2 ex + 1 dx
In Exercises find the indefinite integral. 2 7e* + 4 dx
In Exercises find the indefinite integral. In x² X - dx
In Exercises find the indefinite integral. tan(2/1) 1² dt
In Exercises find the indefinite integral. (tan x)[In(cos x)] dx
In Exercises find the indefinite integral. 1 + cos sin a a - da
In Exercises find the indefinite integral. 1 cos 0 - 1 de
In Exercises find the indefinite integral. - 1 1- (4t + 1)² dt
In Exercises find the indefinite integral. 1 25+4x² dx
In Exercises find the indefinite integral. el/r 1/t 12 1 dt
In Exercises find the indefinite integral. 6 10x x dx
In Exercises find the indefinite integral. 4 4x² + 4x + 65 dx
In Exercises solve the differential equation. dy = dx (ex + 5)²
In Exercises a differential equation, a point, and a slope field are given. (a) Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the
In Exercises solve the differential equation. dy dx = (4 - e²x)²
In Exercises solve the differential equation. (4 + tan² x) y' = sec² x
In Exercises solve the differential equation. dr dt || 10e¹ √1-e2t
In Exercises solve the differential equation. dr dt (1 + e¹)² e³t
In Exercises solve the differential equation. y': = 1 X- x√√4x² - 9
In Exercises evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. *π/4 Jo cos 2x dx
In Exercises evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. TT sin² t cost dt
In Exercises find the area of the region. y = (-4x+6)3/2 15 10 5 y 1 (1.5, 0) 2 -X
In Exercises find the area of the region. y 0.8 0.6- 0.4 3x + 2 x² +9 0.2 1 2 3 4 5 - Х
In Exercises evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. (2/√√3 Jo 1 4 + 9x² dx
In Exercises use a computer algebra system to find the integral. Use the computer algebra system to graph two antiderivatives. Describe the relationship between the graphs of the two antiderivatives.
In Exercises find the area of the region. y² = x²(1-x²) -2 2 -2 y 2 ➤X
In Exercises use a computer algebra system to find the integral. Use the computer algebra system to graph two antiderivatives. Describe the relationship between the graphs of the two antiderivatives.
In Exercises use a computer algebra system to find the integral. Use the computer algebra system to graph two antiderivatives. Describe the relationship between the graphs of the two antiderivatives.
In Exercises find the area of the region. y = sin 2x y 1.0- 0.5- X
In Exercises state the integration formula you would use to perform the integration. Explain why you chose that formula. Do not integrate. [x(x². x(x² + 1)³ dx
In Exercises state the integration formula you would use to perform the integration. Explain why you chose that formula. Do not integrate. S x sec(x² + 1) tan(x² + 1) dx
In Exercises use a computer algebra system to find the integral. Use the computer algebra system to graph two antiderivatives. Describe the relationship between the graphs of the two antiderivatives.
Determine the constants a and b such thatUse this result to integrate sin x + cos x = a sin(x + b).
Show thatThen use this identity to derive the basic integration rule sec x = sin x COS X + COS X 1 + sin x
In Exercises state the integration formula you would use to perform the integration. Explain why you chose that formula. Do not integrate. x² + 1 dx
When evaluatingis it appropriate to substituteto obtainExplain. L₁ -1 x² dx
In Exercises(a) Sketch the region whose area is given by the integral (b) Sketch the solid whose volume is given by the integral when the disk method is used(c) Sketch the solid whose volume is
Using the graph, ispositive or negative? Explain. 5² f(x) dx
In Exercises determine which value best approximates the area of the region between the x-axis and the function over the given interval. (Make your selection on the basis of a sketch of the region
In Exercises determine which value best approximates the area of the region between the x-axis and the function over the given interval. (Make your selection on the basis of a sketch of the region
The graphs of ƒ(x) = x and g(x) = ax² intersect at thepoints (0, 0) and (1/a, 1/a). Find a (a > 0) such that the areaof the region bounded by the graphs of these two functions is 2/3.
In Exercises(a) Sketch the region whose area is given by the integral (b) Sketch the solid whose volume is given by the integral when the disk method is used(c) Sketch the solid whose volume is
(a) Explain why the antiderivative y₁ = ex+C₁ is equivalent to the antiderivative y₂ = Cex.(b) Explain why the antiderivative y₁ = sec² x + C₁ is equivalent to the antiderivative y₂ =
Find the x-coordinate of the centroid of the region bounded by the graphs of y = 5 25x² y = 0, x = 0, and x = 4.
The region bounded by y = e-x², y = 0, x = 0, and x = b (b > 0) is revolved about the y-axis.(a) Find the volume of the solid generated when b = 1.(b) Find b such that the volume of the generated
In Exercises use the integration capabilities of a graphing utility to approximate the arc length of the curve over the given interval. y = x2/3, [1, 8]
In Exercises find the average value of the function over the given interval. f(x) = 1 1 + x²⁹ -3 ≤ x ≤ 3
Consider the region bounded by the graphs of x = 0, y = cos x², y = sin x², and x = √π/2. Find thevolume of the solid generated by revolving the region aboutthe y-axis.
(a) Find(b) Find(c) Find(d) Explain how to find without actually integrating. [ cos³ x dx.
In Exercises find the average value of the function over the given interval. f(x) = sin nx, sin nx, 0≤x≤ π/n, n is a positive integer.
Find the arc length of the graph of y = ln(sin x) from x = π/4 to x = π/2.
In Exercises use the integration capabilities of a graphing utility to approximate the arc length of the curve over the given interval. y = tan TX, [0,1]
Find the arc length of the graph of y = ln(cos x) from x = 0 to x = π/3.
Find the area of the surface formed by revolving the graph of y = 2√x on the interval [0, 9] about the x-axis.
Show that the following results are equivalent.Integration by tables:Integration by computer algebra system: S √√x² + 1 dx = 1/2/(x√/x² + 1 + [n]x + √√x² + 1) + C
Evaluateresults are equivalent.Integration by tables: [² ✓In(9-x) dx In(9-x)+ √In(x + 3)*
(a) Write ∫ tan³ x dx in terms of ∫ tan x dx. Then find ∫ tan³ x dx.(b) Write ∫ tan5 x dx in terms of ∫ tan³ x dx.(c) Write ∫ tan2k+1 x dx, where k is a positive integer, in terms of
In Exercises find the buoyant force of a rectangular solid of the given dimensions submerged in water so that the top side is parallel to the surface of the water. The buoyant force is the difference
In Exercises find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water.Triangle -4- 13
In Exercises find the buoyant force of a rectangular solid of the given dimensions submerged in water so that the top side is parallel to the surface of the water. The buoyant force is the difference
In Exercises find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water.Rectangle -4- 3
In Exercises find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water.Parabola, y = x² -4- I 1 I I 14 1 1
In Exercises the area of the top side of a piece of sheet metal is given. The sheet metal is submerged horizontally in 8 feet of water. Find the fluid force on the top side.3 square feet
In Exercises the area of the top side of a piece of sheet metal is given. The sheet metal is submerged horizontally in 8 feet of water. Find the fluid force on the top side.8 square feet
In Exercises the area of the top side of a piece of sheet metal is given. The sheet metal is submerged horizontally in 8 feet of water. Find the fluid force on the top side.10 square feet
In Exercises find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water.Trapezoid -4- 13 -2-
In Exercises find the fluid force on the vertical plate submerged in water, where the dimensions are given in meters and the weight-density of water is 9800 newtons per cubic meter.Square 2
In Exercises find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water.Semicircle 1 2
In Exercises find the fluid force on the vertical plate submerged in water, where the dimensions are given in meters and the weight-density of water is 9800 newtons per cubic meter.Square -3
In Exercises the area of the top side of a piece of sheet metal is given. The sheet metal is submerged horizontally in 8 feet of water. Find the fluid force on the top side.25 square feet
In Exercises find the fluid force on the vertical plate submerged in water, where the dimensions are given in meters and the weight-density of water is 9800 newtons per cubic meter.Triangle
In Exercises find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water.Semiellipse, y = -√36-9x² -4- 1 13 E I 1
In Exercises the figure is the vertical side of a form for poured concrete that weighs140.7 pounds per cubic foot. Determine the force on this part of the concrete form.Rectangle -10 ft- 12 ft
In Exercises the figure is the vertical side of a form for poured concrete that weighs140.7 pounds per cubic foot. Determine the force on this part of the concrete form.Semiellipse y = -√√16 -
In Exercises the figure is the vertical side of a form for poured concrete that weighs140.7 pounds per cubic foot. Determine the force on this part of the concrete form.Triangle -5 ft 3 ft
In Exercises find the fluid force on the vertical plate submerged in water, where the dimensions are given in meters and the weight-density of water is 9800 newtons per cubic meter.Rectangle 5
Use the result of Exercise 25 to find the fluid force on the rectangular plate shown in each figure. Assume the plates are in the wall of a tank filled with water and the measurements are given in
A circular plate of radius r feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the circle is k feet below the surface of the fluid, where k > r.
In Exercises the figure is the vertical side of a form for poured concrete that weighs140.7 pounds per cubic foot. Determine the force on this part of the concrete form.Rectangle -6 ft- 4 ft
A rectangular plate of heighth feet and base b feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center is k feet below the surface of the fluid, where k >
Use the result of Exercise 23 to find the fluid force on the circular plate shown in each figure. Assume the plates are in the wall of a tank filled with water and the measurements are given in
A cylindrical gasoline tank is placed so that the axis of the cylinder is horizontal. Find the fluid force on a circular end of the tank when the tank is half full, where the diameter is 3 feet and
Repeat Exercise 21 for a tank that is full. (Evaluate one integral by a geometric formula and the other by observing that the integrand is an odd function.)Data from in Exercise 21A cylindrical
Repeat Exercise 27 for a circular porthole that has a diameter of 1 foot. The center is 15 feet below the surface.Data from in Exercise 27A square porthole on a vertical side of a submarine
A square porthole on a vertical side of a submarine (submerged in seawater) has an area of 1 square foot. Find the fluid force on the porthole, assuming that the center of the square is 15 feet below
The vertical stern of a boat with a superimposed coordinate system is shown in the figure. The table shows the widths w of the stern (in feet) at indicated values of y. Find the fluid force against
Approximate the depth of the water in the tank in Exercise 7 if the fluid force is one-half as great as when the tank is full. Explain why the answer is not 3/2.Data from in Exercise 7In Exercises
The vertical cross section of an irrigation canal is modeled by ƒ(x) = 5x²/(x² + 4), where x ismeasured in feet and x = 0 corresponds to the center of thecanal. Use the integration capabilities of
(a) Define fluid pressure.(b) Define fluid force against a submerged vertical plane region.
Explain why fluid pressure on a surface is calculated using horizontal representative rectangles instead of vertical representative rectangles.
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. y y = 4, x = 5
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. 1 y = x² + 1² y=0, x=-1, x=1
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. y = 6 - ²x²₁ 3 y = 7x₁ x = -2, x = 2

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