Calculate by u- Substitution, the follo wing integral definite 3 • cos x • sin x •dx

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Q: cos®xdx CoS Xx, 0.

A: We have to evaluate the integral.

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Q: Evaluate the indefinite integral.

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Q: Evaluate the integral •5 sin(t)dt 6.

A: Given:∫65sintdt

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Q: Find the integral. cos xsin x dx

A: Given, ∫cos3x sin2x dx   We have to find the integral value

Q: Evaluate the following double integral (x² cos y – sin x)dxdy. 0.

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Q: Evaluate the iterated integral: a " cos(2) dy dar.

A: The iterated integral is given as:…

Q: 8 cos" 2πt dt

A:

Q: (x2 + 2x) cos x dx

A: Given,         ∫x2+2xcosxdx

Q: 2n do 3 + sin 0 + cos 0

A: Given integral is ∫02πdθ3+sinθ+cosθ Given z=eiθ We know that  eiθ=cosθ+isinθ e-iθ=cosθ-isinθ So…

Q: | cos' x| dx 3

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Q: 2 Evaluate the definite integral 16sin(t)cos (t) dt.

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Q: Find the indefinite integral cos t dt. 4 cos t dt=

A: We have to find solve

Q: The suitable substitution to evaluate the integral V tan (2x) dx is cos (2x) COS

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Q: Evaluate the definite integral. 4 cos(πt/2) dt

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Q: Evaluate the integral / (6+ sin t)" cos t dt using the substitution u = 6+ sin t. %3D (6+ sin t)ª…

A: Given: ∫6+sint11cost dt To find: ∫6+sint11cost dt using the substitution u=6+sint

Q: 28 t2 sin 2t dt

A:

Q: Evaluate the iterated integral. '1 cos(s³) dt ds Jo Jo

A: Given- ∫01∫0s2coss3 dtds To evaluate- The iterated integral.

Q: evaluate the integral.

A: Let the given integral as

Q: Evaluate the iterated integral. 's4 IT cos(s*) dt ds

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Q: Evaluate the integral. |a cos(6 z) dz =| %3D

A: Topic:- integration

Q: Evaluate the following double integral (x², coS y – sin x)dxdy.

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Q: Evaluate the integral. T/2 cos(t) dt 1 + sin?(t)

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Q: 3. 6x° cos (x*) dx

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Q: Evaluate the double integral ff, cos(x²) dxdyc

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Q: Ja cos³ 0 sin 20 de

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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. integral  cos 3x e x dx

A:

Q: Evaluate the integral cos (x) sin(x) dx using the substitution u = = cos(x). | cos" (x) sin(x) dx 13…

A: topic - integration

Q: Evaluate the integral.  integral cos  - 6  x  dx

A: To evaluate the integral, ∫cos-6xdx Solution: The given integral can be written as,…

Q: Evaluate the integral. cos(0) d0 Tt/2

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Q: Evaluate the integral | (-9 sin(t) – 4 cos(t)) dt Integral =

A:

Q: Use Wallis’s Formulas to evaluate the integral.

A: Wallis's formula for integration for even n: ∫0π/2cosnx dx=12·34… n-1nπ2

Q: Evaluate the integral. cos(6 z) dz %3D

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Q: Evaluate the following integral. TC - -4x coS x dx

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Q: evaluate the triple iterated integral.

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Q: Evaluate the iterated integral. * T/6 cos(e) 7r5 sin(8) dr d0

A: Explanation of the answer is as follows

Q: Evaluate the indefinite integral: 4t cos (t ) dt = %3D

A:

Q: Evaluate the integral cosx dx from T/3 to Tu2 O 0.293 О 0.134 O 0.500 O 0.707

A: To evaluate the definite integral we didn't consider the integral constant at the end of the result.…

Q: Evaluate the integral. sin dt + C -cos O 8 cos +C 1 cos + C O 8 CoS +C

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Q: (cos x Kpxp () I S

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Q: Evaluate the integral / 'cos(æ – In x) dx dy.

A: We need to change the order of double integral

Q: Evaluate the iterated integral. cos(s*) dt ds

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Q: Use the substitution formula to evaluate the integral. 27 3 cos2 x sin x dx 1/3

A: Given that: ∫π/32π3cos2x.sinxdx

Q: Evaluate the definite integral. t3 sin (t4) dt %3D

A: We use substitution method

Q: Evaluate the integral. Tt/3 V1 + cos(2x) dx

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Q: Evaluate the integral.  integral cos  - 4  x  dx

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Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…