Use the rules in Table 5.6 and Equations (2)–(4) to evaluate the inte- grals in Exercises 41–50. 7 dx 41. 5x dx 42. | (1 - v2) dt 43. (2t 3) dt 44. dz 46. 45. (2z – 3) dz 24u du 1/2 3ư du 47. 48. (3x² + x – 5) dx (Зx2 + х — 5) dx 49. 50.

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A: for F = 10 , x = 5

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Q: Explain whether integration by parts may or may not be used to evaluate the integral fx cosx'dx. If…

A: Indefinite Integration

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Q: Use symmetry to evaluate the double integral. Ja+ (1 + x8 sin(y) + y sin(x)) dA, R= [-π, π] x [-π,…

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Q: What is the integrable form of dx? du - 1)- du

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Q: Use u-substitution to evaluate the integral. 3 + 5 Vx dx 3 2 + 5 Vx dx =O

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Q: Calculate the integral (а) dx (*/3 Vtan 0 (b) п/4 -do sin 20

A: Given : (a)  ∫-∞∞x5e-x2 dx    (b) ∫π4π3tanθsin2θdθ

Q: ASAP PLZ Find the moment of inertia with respect to x-axis of the region in the first quadrant,…

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Q: Exampley Consider the following nonlinear sine-Gordon equation Utt-Uxx+5 inu zo subject to the…

A: Solution: Given the Sine-Gordon equation utt-uxx+sinu=0   - - - - - (1) and initially conditions;…

Q: Consider the integral Í dx . For which value of n the error in trapezoidal rule will be less than…

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Q: Givm trapgoidal rule with h =0.25 by Using apploximate the integral.

A: The solution is Given as

Q: What is the moment of inertia of the area bounded by the curve 2x^2 + 2x - y - 2 = 0 and the line y…

A: Image is attached with detailed solution.

Q: In evaluating, 2x cos (2x) dx using integration by parts, identify the portion of the integrand to…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Change the hence order of integlation and evaluate Siny dydx

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Q: Find the moment inertia of the solid formed by revolving about ox the area bounded by a2y=x3, the…

A: Solve the problem

Q: evaluate the intregral of cos2xesin2x dx

A: topic - indefinite integral

Q: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

A: The partial derivative of a two variable function fx,y with respect 'x' can be calculated by…

Q: Sinx Qu(b) Estimate integrel using composite Exapezoidal sule with 0-25

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Q: To integrate by u-substitution, which part of the integrand should you choose as u? S cos de sin² z…

A: We have to find out the substitution

Q: 1 - dx by using properties of improper inte- valuate (r-2)/3

A: Here we have to evaluate I=∫131(x-2)13dx  by using properties of improper integral.

Q: Find the area in the first quadrant bounded by the curve Y = 4–?^2 and the axes using horizontal…

A: Consider the region bounded by the the curve and the axes in the first quadrant

Q: Determine the approximate integration using simple & modified trapezoidal, 1/3 Simpson's and3/8…

A: ∫13e0.5x + sin2x dx, use n = 4a = 1, b = 3so, h = b - an = 3 - 14 = 0.5            xo        xo +…

Q: Find the moment of inertia with respect to x-axis of the area bounded by the parabola y = 4x and the…

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Q: 3 +h (2x) dx By specifying the type of integr rol, examine it by its convegene explaining

A: We are given an improper integral of the first kind by the following.…

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Q: Eváluáté thè intégral. 7/4 (7 cos ti+ 5 sint j) dt -n/4 O 7N2 i+ 52 j O 7N2 i O 52 i

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Q: Make a substitution to express the integrand as arational function and then evaluate the integral.…

A: Given: ∫x3x2+13dx

Q: * Using integration by parts, the integral sec³dx is equal to 1 1 - secxtanx +In|secx +tanx| + C 2 1…

A: Use by parts method of integration

Q: Find the limits of integration in cylindrical

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Q: Scos* y sin ydy

A: Given problem:- ∫ cos4(y/2)sin(y/2) dy

Q: Find the moment of inertia of the area in the first quadrant bounded by the curves y = 9 – x² and y…

A: Moment of inertia bounded by the curves y2 and y1 about y-axis is  Iy=∫abx2(y2-y1)dx Consider the…

Q: integral arctan4t dt

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Q: Find the work done in stretching a spring of natural length 8 cm, from 10 cm to 13 cm. Assume a…

A: Given information:- Find the work done in stretching a spring of natural length 8 cm, from 10 cm to…

Q: What is the antiderivative of the integrand dx ? 2e*

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Q: Approximate the integral | dx using 4 trapezoids .2 1

A: Introduction: The formula for the trapezoidal rule is given by, ∫aby(x)dx=h2y0+yn+2(y1+y2+...+yn-1)

Q: Consider the integral dx . For which value of n the error in trapezoidal rule will be less than…

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Q: 1 dx is an improper integra 2 3x

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Q: sin x dx B) - 7 1+ 2 1+ A) -(1+ 2) 7 C) - 2 1+ D) 4 8

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Q: Find the value of 'h' in 8 dx evaluating by 1+x Trapezoidal rule braking in 24 intervals. 1.25 0.25

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Q: ⌠13(e0.5x+sin2x)dx, use n=4

A: We will answer the first question as you didn't mention any. Please resubmit the other question…

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.

A: From the given graph, The function y = k x13  limits from x = a  to  x = b

Q: Change the order of integration 2 rIn(r)+1 f(r,y) dy dx Ji Ji

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