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mathematics
calculus 4th

Questions and Answers of Calculus 4th

Determine whether the improper integral converges and, if so, evaluate it. 00 12 e-2x dx
Calculate SN given by Simpson’s Rule for the value of N indicated and compare with the actual value of the integral. So sin x dx, N = 6
Evaluate using the appropriate method or combination of methods. Sse sec²0 tan+ 0 de
Determine whether the improper integral converges and, if so, evaluate it. al dx L +0.2 X
Calculate SN given by Simpson’s Rule for the value of N indicated. S dx x4 + 1' N = 6
Evaluate using the appropriate method or combination of methods. (6x + 4) dx x² - 1
Determine whether the improper integral converges and, if so, evaluate it. 00€ 2 xdx
Calculate SN given by Simpson’s Rule for the value of N indicated. cos(x²) dx, N = 6
Evaluate using the appropriate method or combination of methods. J4 dt (t²-1)²
Determine whether the improper integral converges and, if so, evaluate it. *00 J4 e-3x dx
Calculate SN given by Simpson’s Rule for the value of N indicated. S'e ex2² dx, N = 4
Evaluate using the appropriate method or combination of methods. S de COS 0
Determine whether the improper integral converges and, if so, evaluate it. ~00 S 4 e³x dx
Calculate SN given by Simpson’s Rule for the value of N indicated. f² e ² ax ex dx, N = 6
Evaluate using the appropriate method or combination of methods. S sir sin 20 sin²0 de
Determine whether the improper integral converges and, if so, evaluate it. -00 e³x dx
Evaluate using the appropriate method or combination of methods. S₁ In(4- 2x) dx
Calculate SN given by Simpson’s Rule for the value of N indicated. J1 Inxdx, N = 8
Determine whether the improper integral converges and, if so, evaluate it. J1 dx (x - 1)²
Calculate SN given by Simpson’s Rule for the value of N indicated. S √x+1dx, N = 8
Evaluate using the appropriate method or combination of methods. far (In(x + 1))² dx
Determine whether the improper integral converges and, if so, evaluate it. S dx √3 - x
Calculate SN given by Simpson’s Rule for the value of N indicated. π/4 SOTA tan 0 de, N = 10
Evaluate using the appropriate method or combination of methods. S si sin 0 de
Determine whether the improper integral converges and, if so, evaluate it. S -4 dx (x + 2)¹/3
Calculate SN given by Simpson’s Rule for the value of N indicated. S² (x² + 17-1/³ dx (x²+1)-¹1/3 dx, N = 10
Evaluate using the appropriate method or combination of methods. f cos¹ (9x - 2) dx
Determine whether the improper integral converges and, if so, evaluate it. 00 dx 1 + x So 0
Calculate the approximation to the volume of the solid obtained by rotating the graph around the given axis.y = cos x; [0, π/2]; x-axis; M8
Evaluate using the appropriate method or combination of methods. π/4 sin 3x cos 5x dx
Determine whether the improper integral converges and, if so, evaluate it. L -00 xe dx
Evaluate using the appropriate method or combination of methods. S sin 2x sec² x dx
Calculate the approximation to the volume of the solid obtained by rotating the graph around the given axis.y = cos x; [0, π2]; y-axis; S8
Determine whether the improper integral converges and, if so, evaluate it. z(zx + 1) xdx S.. 00%
Calculate the approximation to the volume of the solid obtained by rotating the graph around the given axis.y = e−x2; [0, 1]; x-axis; T8
Evaluate using the appropriate method or combination of methods. S √tan x sec² x dx
Evaluate using the appropriate method or combination of methods. f(sec. (sec x + tan x)² dx
Determine whether the improper integral converges and, if so, evaluate it. J3 xdx √x - 3
Calculate the approximation to the volume of the solid obtained by rotating the graph around the given axis.y = e−x2; [0, 1]; y-axis; S8
Evaluate using the appropriate method or combination of methods. f sin³ sin5 0 cos³ 0 de
The back of Jon’s guitar (Figure 16) is 19 in. long. Jon measured the width at 1-in. intervals, beginning and ending 1/2 in. from the ends, obtaining the resultsUse the Midpoint Rule to estimate
Determine whether the improper integral converges and, if so, evaluate it. Г 00 xe-3x dx
Use Simpson’s Rule to determine the average temperature in a museum over a 3-hour period if the temperatures (in degrees Celsius), recorded at 15-minute intervals, are 21, 21.3, 21.5, 21.8, 21.6,
Determine whether the improper integral converges and, if so, evaluate it. S xe dx -00
Evaluate using the appropriate method or combination of methods. Scot³: cot’ xesc xdx
Scientists estimate the arrival times of tsunamis (seismic ocean waves) based on the point of origin P and ocean depths. The speed s of a tsunami in miles per hour is approximately s = √15d, where
Determine whether the improper integral converges and, if so, evaluate it. S 0₁ dx √9 - x²
Evaluate using the appropriate method or combination of methods. Sc cot² xcsc² x dx
Determine whether the improper integral converges and, if so, evaluate it. S' 0₁ e √x dx √x V
Use S8 to estimate ∫π/20 sin x/x dx, taking the value of sin x/x at x = 0 to be 1.
Evaluate using the appropriate method or combination of methods. π/2 cot² - de z de
Evaluate using the appropriate method or combination of methods. T/2 Jx/4 cot² xcsc³ xdx
Determine whether the improper integral converges and, if so, evaluate it. e√x dx √x +00 Se
Calculate T6 for the integral I = ∫20 x3 dx.(a) Is T6 too large or too small? Explain graphically.(b) Show that K2 = |ƒ"(2)| may be used in the Error Bound and find a bound for the error.(c)
Evaluate using the appropriate method or combination of methods. J4 6 dt (t− 3)(t + 4) -
Compute ∫1.999990 1/(4 − x2)3/2 dx
Determine whether the improper integral converges and, if so, evaluate it. S 10 sec 0 de
Evaluate using the appropriate method or combination of methods. dt (t - 3)²(t+4) Sa
State whether TN or MN underestimates or overestimates the integral and find a bound for the error (but do not calculate TN or MN). 1 S + = = d.x. X - dx, T10
Determine whether the improper integral converges and, if so, evaluate it. roo So sin x dx
Evaluate using the appropriate method or combination of methods. S √x² +9dx
State whether TN or MN underestimates or overestimates the integral and find a bound for the error (but do not calculate TN or MN). S² e-x/4 dx, T20
Determine whether the improper integral converges and, if so, evaluate it. π/2 So 0 tan x dx
Evaluate using the appropriate method or combination of methods. dx x√x² - 4
State whether TN or MN underestimates or overestimates the integral and find a bound for the error (but do not calculate TN or MN). S J1 Inxdx, Mo
Determine whether the improper integral converges and, if so, evaluate it. So Inxdx
Evaluate using the appropriate method or combination of methods. -27 8 x dx x + x2/3
State whether TN or MN underestimates or overestimates the integral and find a bound for the error (but do not calculate TN or MN). π/4 cos x, M20
Determine whether the improper integral converges and, if so, evaluate it. dx J1 ₁ x lnx
Evaluate using the appropriate method or combination of methods. dx x³/2 + ax¹/2 S;
Use the Error Bound to find a value of N for which error (TN) ≤ 10−6. If you have a computer algebra system, calculate the corresponding approximation and confirm that the error satisfies the
Determine whether the improper integral converges and, if so, evaluate it. In x dx x² 0
Evaluate using the appropriate method or combination of methods. dx (x-b)² + 4 S
Use the Error Bound to find a value of N for which error (TN) ≤ 10−6. If you have a computer algebra system, calculate the corresponding approximation and confirm that the error satisfies the
Determine whether the improper integral converges and, if so, evaluate it. 00* S In x zx dx
Evaluate using the appropriate method or combination of methods. (x²-x) dx (x + 2)³ SOR
Use the Error Bound to find a value of N for which error (TN) ≤ 10−6. If you have a computer algebra system, calculate the corresponding approximation and confirm that the error satisfies the
Let I = ∫∞4 dx/(x – 2)(x – 3)(a) Show that for R > 4,(b) Then show that I = ln 2. R dx J4 (x-2)(x-3) In |R-3 |R-2] In 1 2
Evaluate using the appropriate method or combination of methods. (7x² + x) dx (x-2)(2x + 1)(x + 1)
Use the Error Bound to find a value of N for which error (TN) ≤ 10−6. If you have a computer algebra system, calculate the corresponding approximation and confirm that the error satisfies the
Evaluate using the appropriate method or combination of methods. 16 dx (x - 2)²(x²+4) S
Evaluate the integral I = ∫∞1 dx/x(2x + 5).
Compute the Error Bound for the approximations T10 and M10 to∫ 30 (x3 + 1)−1/2 dx, using Figure 17 to determine a value of K2. Then find a value of N such that the error in MN is at most
Evaluate using the appropriate method or combination of methods. f dx (x² +25)²
Evaluate I =∫10 dx/x(2x + 5) or state that it diverges.
(a) Compute S6 for the integral I = ∫10 e−2x dx.(b) Show that K4 = 16 may be used in the Error Bound and compute the Error Bound.(c) Evaluate I and check that the actual error is less than the
Evaluate using the appropriate method or combination of methods. dx x² + 8x + 25 S
Evaluate I = ∫∞2 dx/(x + 3)(x + 1)2 or state that it diverges.
Determine whether the doubly infinite improper integral converges and, if so, evaluate it. Use definition (2). 00€ J xdx 1 + x² -00
Calculate S8 for ∫51 ln x dx and calculate the Error Bound. Then find a value of N such that SN has an error of at most 10−6.
Find a bound for the error in the approximation S10 to ∫30 e−x2 dx (use Figure 18 to determine a value of K4). Then find a value of N such that SN has an error of at most 10−6. у 12- -8 + 2 3
Evaluate using the appropriate method or combination of methods. dx x² + 8x + 4 S
Determine whether the doubly infinite improper integral converges and, if so, evaluate it. Use definition (2). 00 -00 e-lx dx е
Evaluate using the appropriate method or combination of methods. x + 4 x³ 2x²x+2 S= dx
Use a computer algebra system to compute and graph ƒ(4) for ƒ(x) = √1 + x4, and find a bound for the error in the approximation S40 to ∫50 ƒ(x) dx.
Determine whether the doubly infinite improper integral converges and, if so, evaluate it. Use definition (2). 00 J-00 xe dx
Evaluate using the appropriate method or combination of methods. SANT 0 1² √1-1² dt
Determine whether the doubly infinite improper integral converges and, if so, evaluate it. Use definition (2). dx S Lux (1² + 1)³/2 -00
Use a computer algebra system to compute and graph ƒ(4) for ƒ(x) = tan x − sec x, and find a bound for the error in the approximation S40 to ∫π/40 ƒ(x) dx.
Evaluate using the appropriate method or combination of methods. dx x4 √√x² + 4 S

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