Evaluate the integral using integration by parts with theindicated choices of u and dv .   ∫θ Cos θ dθ  ; u = θ , dv= Cos θ dθ

Q: Evaluate the integral by making an appropriate change of variables. I| 3 cos( 9 ( ) da where R is…

A: Given ∫∫R3cos9y-xy+xdAWhere R is the trapezoidal region with vertices 7,0, 9,0, 0,9, 0,7

Q: Use Romberg integration to find an 0(h*) approximation for the following integral | In(x² + 3)dx I =

A: Consider the given integral which is required to solve.

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: Consider the integration ∫x3x2+9dx Substitute x=3tanθ ⇒dx=3sec2θdθ Hence,…

Q: r? + I dx

A: NOTE: Refresh your page if you can't see any equations. . ................(1) substitute…

Q: Evaluate the integral using the given substitution. Jx cos (6x?) dx, u=6x? x2 O A. sin (6x?) +C 2 1…

A: As per our guidelines we need to solve only one question.please repost the remaining questions as…

Q: Evaluate the integral by choosing a convenient order of integration: x cos(xy) cos' (Tx) dA; R= x…

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Q: Given the integral " Se F(x, y) dydx, which ONE of the following integrals is equivalent?

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Q: Use contour integration to compute the following integrals. (a) 1. 2π cos(20) dv 5+4 cos v

A: (a) Given integral ∫02πcos(2ϑ)dϑ5+4cosϑ. The objective is to compute the integral by using contour…

Q: x sin z dz dy dx 0, y

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Q: Evaluate the integral using the Integration by Parts formula with u = 2x + 3, dv = e*dx. (Use…

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Q: Choose five other iterated integrals that are equal to the given iterated integral. r2 f(х, у, 2) dz…

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Q: Evaluate the integral using the following values. x dx = 60 x dx = 6, dx = 2 J2 %3D 5x dx J2

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Q: evaluate the integral using the Integration by Parts formula with the given choice of u and dv.

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Q: Use the integration by parts to evaluate the following integral by assuming u = COS 2 dx (cos a + a…

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Q: Evaluate the integral. (Use C for the constant of integration.) sin (0) cos (0) de

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Q: Evaluate the integral by using the substitution u = 1 + e*. 1 – e* %3D dx 1+ e*

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Q: Evaluate the integral and interpret it as the area of a region. T/2 14 sin(x) – 4 cos(2x)| dx

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Q: tan(x)dx, Ind: u = cos(z)

A: We have to calculate the given integral: ∫tan x dx We know the identity, tan x=sin xcos x Therefore,…

Q: Evaluate the integrals. ∫sin z sin (cos z) dz

A: Consider the given integral ∫sinzsincoszdz

Q: Evaluate the integral using the given substitution. (Vx cos (x3/2- 4) dx

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Q: 1. xe 2* dx; u = x, dv = e 2× dx

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Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

A: We have to evaluate the integral by first modifying the form of the integrand ∫ [ln(e8x) + ln(e-8x)]…

Q: Evaluate the integral in the form a sin(u(x)) + C for an appropriate choice of u(x) and constant a:…

A: given,         A=∫x2cosx3+1dx

Q: Evaluate the integral cos(x?) dæ dy by reversing the order of integration.

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Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: Topic -Integration

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

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Q: Evaluate the integral by choosing a convenient order of integration: x cos(ry) cos (Tx) dA; R= x (0,…

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Q: Evaluate the integral using the given substitution. Jx cos (5x?) dx, u=5x? O A. sin (5x2) +c 1 O B.…

A: Note:Since you have asked multiple question, as per our guidelines we are supposed to answer only…

Q: Evaluate the integral and interpret it as the area of a region. •T/2 14 sin(x) – 4 cos(2x)| dx

A: Given that integral ∫0π24sin(x)-4cos(2x)dx First, we have to split integral because,…

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

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Q: evaluate the integral in the form a sin(u(x)) + C for an appropriate choice of u(x) and constant a.

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Q: Find the integral using an appropriate trigonometric substitution. J ×V36 - x* dx

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: We have to solve the problem

Q: Evaluate the integral cot2x dx J Tcot?x – 15

A: We will evaluate the given integral as shown below

Q: Evaluate the integral and interpret it as the area of a region. T/2 |4 sin(x) – 4 cos(2x)| dx

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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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 by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: The resulting integral of S dx is In + e Tan"1+ C where a, b, d, and e are integgrs. x+x²+4x+4 What…

A: Differentiate the result of the integral:…

Q: Evaluate the integral as a number, o, or –∞ or enter DNE if there is no limit. sin(x) dx = -cos(t) +…

A: Given: To evaluate the integral: ∫0∞sin(x) dx   Formula used: ∫0∞f(x) dx=lima→∞∫0af(x) dx

Q: 1. dæ; u = x, dv = e2¤ dx

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Q: Evaluate the integral using the given substitu Sxcos (5x?) dx, u=5x? dx, u= 5x sin (5x?) +c О в. sin…

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Q: Evaluate the integrals .SiPi+7 j+(t+1)k] 4 S (sinti+(1+cost)j] -a4

A: In the given question, we have to find the integral of  ∫01[t3i+7j+(t+1)k] ∫-π4π4[sinti+(1+cost)j]

Q: Which of the following integrals represent the area enclosed by the smaller loop of r = 1 +2 sin 0?

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Q: Evaluate the integral using integration by parts. [8 e 20 sin 20 de

A: The formula for the integration by parts is ∫udv=uv-∫vdu The given integral is ∫8e2θsin2θdθ

Q: By reversing the order of integration, evaluate the following integral. To ²² x cos (y²) dy dx. co

A: The given problem is to evaluate the given double integral by reversing the order of integration.

Q: (e) [ 4z. 4x · cos(2-3x)da

A: Topic:- application of integration

Q: Evaluate the integral by choosing a convenient order of integration: x cos(xy) cos' (Tx) dA; R 0, x…

A: Given

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.