Differentiating Integrals Under mild continuity restrictions, it is true that if F(x) = g(t, x) dt, then F'(x) = 8,(t, x) dt. Using this fact and the Chain Rule, we can find the derivative of rf(x) F(x) g(t, x) dt by letting G(u, x) = | 8(t, x) dt, where u = f(x). Find the derivatives of the functions in Exercises 59 and 60. 59. F(x) = Vª + x³ dt 60. F(x) /ß + x² dt

Q: 5. (a) Use integration by parts to find f xe-3x dx. +00 -3x (b) Determine whether the improper…

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Q: how I calculate the definate integral 3x^2-e^2x(dx) on the interval ln3 to 0

A: To find the definite integral

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) Jx x5/2 In(x) dx

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Q: (5) Find the indefinite integral (a)fVtan x sec'dx aun 2x sec' 2xdx sin x (c)) cos'x 1 cos-de

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Q: We must integrate y = (8x-x2)-(2x) = 6x-x². The limits on the integral correspond to the smallest…

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Q: Find the indefinite integral using integration by parts with the given choices of u and dv. [x x cos…

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Q: sinh x tex cosh x + ex In the indefinite Integral in(cosh x + e*)- sinh x + ex A cosh x + ex sinh x…

A: In this question, we want to know the integrand of the given Integral.

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. x cos 7x…

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Q: Evaluate the integral if it converges ∫ from 0 to infinity e^-x cos(4x)dx

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Q: Suppose we want to evaluate the definite integral, t/1+ 7t dt using the substitution, u = 1+ 7t.…

A: Here is the solution:

Q: Find the indefinite integral. (Use C for the constant of integration.) |zV 16z2 - 81 zp

A: ∫1x2+a2 dx = 1aarc tan(xa)+C

Q: Find the general indefinite integral. (Use C for the constant of integration.) x3 + 4 x2 ) dx

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Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: Given: ∫(1,0,0)(0,1,1)sinycosxdx + cosysinxdy+dz To Show: (a). Differential forms in the integral…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.)…

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Q: 3. Find the indefinite integral. (Use C for the constant of integration.) Ssin(3x) cos(3x) dx

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Q: If the integral diverges, indicate that using the checkbox. 6 dx The integral diverges x(x + 1)

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Q: Express the limit as a definite integral on the given interval. lim n → ∞  n [2 − 5(xi*)2 + 6(xi*)4]…

A: Given query is to find the integral form of limit.

Q: In(2 x) dx =; x³ In( 2 x) - +C x e dx = -2 (2 +x) e +C

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Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

A: The given integral is: ∮Cz2+5z2-6iz-5dz, where C is the circle z-6i=1.3 Cauchy Integral formula: Let…

Q: show that the differential forms in the integralsare exact. Then evaluate the integrals

A: Show that the differential forms in the integrals are exact. Then evaluate the integrals.…

Q: Let f(x) = x ( +2)* and calculate %3D f(x) dr by using integration by substitution. What was your…

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Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

A: To find the integration

Q: Use fundamental theorem to evaluate the definite and differentiating integrals on the following…

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Q: Prove that X+1 Cothx=-In

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) COS X dx (sin x)20

A: Given, ∫cosxsinx20dx We have to evaluate the indefinite integral.

Q: sin(x) dx =-x² cos(x)+2 cos(x)+ 2 x sin(x) + C e* s in(x) dx= 1 cos(x) + e* sin(x)+ C e*

A: Topic = Integration

Q: In this situation, finding the indefinite integral is most easily achieved using the method of…

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Q: (0,0) to (1,1) along two paths: first from (0,0) to (1,0) to (1,1), and then from (0,0) to (0,1) to…

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Q: Find the indefinite integral of S Option 1: Option 2: Option 3: x ln |1x|+C x ln x + C In 1-x| X + C…

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Q: The integral of ƒ In(ln(x))dx can not be expressed as a finite sum of functions. What do we call…

A: It is called as non elementary integral

Q: the point of discontinuity on(0, co), the Fourier Sine integral converges to: None (**) + f(x¯)] **)…

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Q: integral from 2 to 3 of (x^3 - 2x) dx / x-1

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Q: show that uuX)-X (1+x*J% I'sasolutionto integralequation ux)=X-sinh (x-t)u (t) dt

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Q: 1 1-x Change the order of integration and then evaluate the integral: fx dydx X Jx-1

A: We draw the graph of the limits of the integration then we change the order accordingly

Q: Determine the value of the integral: integral sign:  (x^2)(e^-x^3)

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Q: sinh x tex cosh x + ex In the indefinite Integral Sin(cosh x + ex)- sinh x tex A cosh x + ex sinh x…

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Q: Find the general indefinite integral. f x^4 + 4x + 1 / x  dx

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Q: x° sin(x³) In(4 + cos(x³)) if x 10° ya. 00 Determine whether or not the improper integral dx…

A: We have to use comparison test here.

Q: To evaluate: The integral function x2 +x + 1 -dx. (x² + 1)²

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Q: The Mean Value Theorem for Integrals guarantees the existence of a special point on the graph y = 2x…

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Q: Express the limit as a definite integral on the given interval. cos(x;) lim n-0 i = 1 Дх, [2л, 5л]…

A: Given limn→∞∑i=1ncos(xi)xi∆xi in the interval [2π,5π]We need to express the limit as a  definite…

Q: 8. Consider the indefinite integral |x°(x² + 5) dx. = x7 +5. x6 and dv = (x" + (a) Evaluate the…

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Q: (2+ln² x) 2. S: -dx x(1-In x)

A: As per rules supposed to solve only one problem at a time so please post the remaining question as a…

Q: 1. Evaluate the integral. (Use C for the constant of integration.) Show ALL work. xp^

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Q: 9. Use the substitution u = x° + 2x to find the following indefinite integral. Check your answer by…

A: The integral is given by,

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3)…

A: Given : ∫( 0 , 0 ,0)( 1, 2, 3)  3 x2y dx + ( x3 - z3 ) dy - 3y z2 dz

Q: Only piecewise continuous functionsf (x) on every finite interval (0, 0) such that 00 | S(x)| dxis…

A: According to the condition of convergence for Fourier integral,  Let f and f' be piecewise…

Q: 2. Evaluate the integral. (Use C for the constant of integration.) Show ALL work. St sin(t) cos(t)dt

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Q: lim n→∞  n xi ln(1 + xi2) Δx, [0, 2]   i = 1  2   0     dx

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Q: et * e-t Compute the convolution integral.

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