Calculate the following integral: 4 I V16 - x dx .2 0.

Q: et dx 1+ea

A: Given, The integral ∫ex1+exdx We have to evaluate the integral.

Q: Evaluate the interated integral: LS-² x² sin(y) dy dx

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Q: Find the most general antiderivative or indefinite integral. (a) / -3t2 + evt3 dt Vi 4 dx 3V - x² 2…

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) yV 6 +…

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Q: Evaluate the integral by making the given substitution.   ∫ Sinπ x dx , u =π x

A: Given integral is We will use the following substitution to evaluate the integral.

Q: use the indicated substitution to evaluate the integral.

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Q: luate the following definite integral 2 dx J V3 – x + Vx

A: In this question, the concept of integration is applied. Integration Integration is a method of…

Q: T 11x + 29 dx The integral is equal to

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Q: Evaluate the integral. (Use C for the constant of integration.) | e20 sin(30) de

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Q: Evaluate the integral p.v. J e2ix -dx. 00 x+1

A: We can apply Cauchy integral theroem to find the integral.

Q: Calculate the integral approximations T6 and M6 for ∫sec^2x dx [0,pi/7]

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Q: Evaluate the indefinite integral. 1x - 3 dx J (læ2 – 6x + 4)3 Answer = +C

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Q: Reverse the order of integration and then evaluate the integral. 5 5 sin y dy dx 0 x

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Q: c) Seax.Sinbx. dx =? Calculate the integral

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Q: Evaluate the integral: x sin(y) dy dx

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Q: dx '1 x[13+ln(x²)]

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Q: dx Væ(x+1)

A: Let I=∫14dxxx+1. Put x=t2 and differentiate it with respect to x. ddxx=ddxt21=2tdtdxdx=2tdt

Q: calculate the integral in terms of the inverse hyperbolic functions.

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Q: Evaluate the integral. (Use C for the constant of integration.) 4 sin Vx xp

A: To evaluate the given integral.

Q: Use integration by parts to evaluate the integral.

A: Apply integration by parts,

Q: Use a double integral to fi and y = 3(x+ 1).

A: Given the two curves y=x2+2x+1y=3(x+1)

Q: Reverse the order of integration in order to calculate the following integral: 2 1+x4 0 dx dy.

A: We can evaluate the given integral by using the integral formulas.

Q: LL L dx dy dz 4. Evaluate the triple integral :

A: First Evaluate integration w r to x  Second integration w r to y Third integration w r to z

Q: Consider the following integrals: dt i). S" Şi + sint' ii). S° a4 cost dt where a > 2, iii). Int…

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Q: 1. dx (т + 1) (2 + 1) 1

A: Explanation of the answer is as follows

Q: A/2 x+! I Į sin x dy dx -1 0 96.

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Q: calculate the integral in terms of the inverse hyperbolic functions.

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Q: x+1 dx

A: We need to integrate∫x3+1xdx

Q: ∫ (e3x+5ex+2  divided by  ex) dx a.) Compute the integral

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Q: dx 1 = J Jaz-x2

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Q: Find the indifinite integral. 2x +1) ex²+x dx

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Q: Evaluate the integral

A: ∫1+x2xdx Put, x=tanθ⇒1=sec2θ·dθdx⇒dx=sec2θ·dθ

Q: Evaluate the integral , dx 1+ e* using the substitution u = 1+ e". %3D et dx 1+ e"

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Q: Evaluate the integral. eX dx V1-e2x Select one: O A. sec (e) + C O B. sin (e) + C O C.-2V1-e2x + C O…

A: We evaluate the given integral by substitution.

Q: Q2. Evaluate the iterated integral by changing the order to dx dy. eu dy dx

A: For reversing the integration order, we will replace the limit of x and y with interchangeably. Then…

Q: Evaluate the triple integral 5 z sin x dy dx dz 3.

A: Given:

Q: 2 dx. x? +1 34. Evaluate the improper integral

A: Use limit method

Q: 。vマ dx ナ○

A: To evaluate the integral: ∫1∞e-xxdx Solution: Let substitute t=x. dtdx=ddxxdtdx=12x2dt=1xdx When x→∞…

Q: Evaluate the following integral. * R/2 sinx sin y dz dx dy 0 0 0

A: Given Integral is  ∫0π∫0π2∫0sinxsinydzdxdy

Q: a. Sx² e3*dx b. St sin t dt

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Q: Evaluate the integral. (Use C for the constant of integration.) | 9t sin?(t) dt

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Q: Evaluate the integral. (Use C for the constant of integration.) sin(t) dt os°(t) coS

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Q: Evaluate the integral.

A: Integral:     ∫0x3 ye-yx dxWe need to do by parts    ∫uvdx=u∫vdx-∫[ddx(u).∫vdx]dx

Q: Use the Method of Substitution to find the indefinite integrals: t3et“ dt dx x VIn x

A: The given integral,a) ∫t3 et4 dtb) ∫9xln x4dx

Q: V.r dx.

A: The given indefinite integral is: ∫xx-x23dx

Q: Vx? – 1 dx 4

A: