Transform the integral fo So sin o ne do de by the substitution x = sin o cos 0, y = sin o sin 0 and then find its value.

Q: cos(8) cos (sin(0)) de

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Q: | sec®t tan? t dt

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Q: Evaluate the integral. cos(z) dz sin? (z)

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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: Transform the integral fo o sin o sin 0 do de by the substitution x = sin o cos 0, y = sin ø sin 0…

A: Solution: The given integral is I=∫0π2∫0π2sinϕsinθdϕdθ The substitution is x=sinϕcosθ, and…

Q: Use the Table of Integrals to evaluate the integral. T4 - 9 sin e sin 20 de 4 – 9 sin 0 |

A: We use substitution to integrate the given function.

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: Evaluate the integral. cos y dy sin 2y + 2 sin y – 3

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Q: Consider the integral sin(5z) d: Applying the integration by parts technique, let and du x dz Then…

A: The by parts formula of integration is ∫udv=uv-∫vdu.

Q: a) Evaluate the integrals using appropriate substitutions. dx Sino i)S i) f de Cos? 8+1 1+16x2

A: as per our guidelines I am solving only first question with both parts a(i) ∫dx1+16x2ii ∫sinθcos2θdθ

Q: r430 sin x 160 cos2 x(16-sec² x)

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Q: Evaluate the integral given. sec(2a)tan(2a)dx +C %3D

A: ∫ sec(x)tan(x) dx =sec(x)+C

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

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Q: The resulting integral of sin-cos-sino de has the form -F(@) +C What should be the value of e to…

A: We know that integration of sinx is - cosx and we know that trigonometry relation is  Sin2x =  2sinx…

Q: Evaluate the integral by making the given substitution. (U | cos12 0 sin 0 d0, u = cos 0

A: Given : ∫cos12θsinθdθ

Q: |a" cos(2°) da = +C. %3D Hint: First make a substitution and then use integration by parts to…

A: Consider the given integral ∫x11cosx6dx. Let u=x6. That implies, du=x6dxdu=6x5dxdx=du6x5 Then, the…

Q: Calculate the double integral. 9x sin(k + y) dA, R = 0, 풍핑x [o, 플]

A: First we will evaluate the inner integral wrt 'y' and then evaluate wrt 'x'.

Q: Evaluate the integral using the given substitution. 15) 1- sin cos dt, u = 1 - sin 13 1 - sin + C A)…

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

A: Consider the given integral ∫sinzsincoszdz

Q: Evaluate the integral using the given substitution. Sx cos (10n2) dx, u = 10x² sin (10x²) - C sin…

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

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Q: Use the fact that cos(z) = R(eiz) = (eiz + e-iz)/2 to find the integral of (e3xcos(4x))dx.

A: Here the given integral in not in the complex form so we calculate the integral as it is given in…

Q: j x. sin x d

A: Integration: I=∫x.sin x dxWe need to solve this by by parts method.   ∫u.v dx=u∫v dx-∫[ddx(u) .∫v…

Q: Evaluate the integrals: A: So So x sin y dy dx

A: ∫0π∫0xx siny dy dx

Q: Find the integral for positive integers m, n sin mx cos nx dx -T

A: NOTE: Refresh your page if you can't see any equations. . use the formula

Q: Find the integral a 3x? cos (x ) dx where a is some positive real number.

A: Given : ∫0a3  3x2cosx3dx , where a is some positive real number

Q: Find the value of the integral ∫∫R  and cos(x) cos(y) dA, where R=

A: We need to evaluate  ∫∫cos(x)cos(y)dA over region R=(x,y)| 0≤x≤π2,  0≤x≤π2

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. 5- sin cos dt, u= 5- sin- cos 1 O A. 5- sin 3 t…

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Q: 3(sin y– cos y)°dy cos y

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Q: Transform the integral fo So? sin o sin 0 do do by the substitution r = sin o cos 0, y = sin o sin 0…

A: Given ∫0π2∫0π2sinϕsinθdϕdθand x=sinϕcosθ, y=sinϕsinθ

Q: Evaluate the iterated integral. 5 (T/2 r cos e dr de dz

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Q: Evaluate the integral. NÓTE: Enter the exact answer. xy" dy 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 in the form a sin(u(x)) + C for an appropriate choice of u(x) and constant a.

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Q: sec? e de. 1- tan e Evaluate the improper integral:

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Q: Evaluate the integral. * T/2 sin³x cos y dx

A: Using identity         Sin2x+cos2x=1

Q: - sin(y) dy: cos(y) + 7 Consider the integral- This can be transformed into a basic integral by…

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Q: Evaluate the integral L I sin (y²) dy dr.

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Q: The best substitution to use for the integral sin z V1+ cos z dx

A: when we substitute, u = 1 + cosx then the value of du = - sinx dx

Q: |a° cos (2") dz = +C. Hint: First make a substitution and then use integration by parts to evaluate…

A: Given query is to find the integration of the expression.

Q: Evaluate the integral from 0 to pi/2 6 sin5(t) cos(t) i + 3 sin(t) cos2(t) j + 8 sin(t) cos(t) k

A: Given:  ∫0π26sin5tcosti+3sintcos2tj+8sintcostkdt To determine: The value of given integral.

Q: 3(sin y- cos y) chy cos y

A: First we use (siny - cosy) 2 =sin2 y + cos2 y -2sinycosy Then using u substitution let u =sexy +…

Q: eiz 0o cos x dx? cos z Can you use - 1+ z2 instead of - 1+ z2 to obtain the integral for Jo 1+x²

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Q: evaluate the integral using substitution method sin√w/√w dw

A: The given integral beI. I=∫sinwwdw. The most important step is to convert  variable such that the…

Q: Set up the integral for the common interior of r1 and r2.  r1 = 3 + 3 cos theta  r2 = 3 sin theta

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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: The resulting integral of form --F(0) +C. de has the What should be the value of e to make F(@)=0?

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Q: Evaluate the integrals

A: We have to evaluate the definite integral: ∫-ππ1-cos2 t32dt We know the trigonometric identity, cos2…