Evaluate the definite integral 15 cos(t)dt:

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A: The given integral is, Let u = cos t. Then, du = –sin t dt. The upper limit changes to u = cos(π/6)…

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A: Hello,Thank you for the question. As per our guidelines, we are allowed to answer one question. So…

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A: Evaluate the integral as follows.

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A: As per the company guidelines we can solve first three parts. I hope that the given solution will…

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A: Consider u=lnt. Then, du=dttdt=tdu

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

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A: We have to find solve

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A:

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A: We need to evaluate the following integralI= ∫5t2sintdt

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A: The width of the interval [-1,3] is (3-(-1))=4If there are n sub intervals. Then the width of each…

Q: Evaluate the definite integral (cos(t), sin(t))dt

A:

Q: Evaluate the definite integral. 5 cos(πt/2) dt

A: We have to find

Q: Evaluate the definite integral. 1 6 cos(at/2) dt

A: Given:        ∫016cosπt2dt Taking constant out      =6∫01cosπt2dt substitute u=πt2…

Q: (8ti + tj – k) dt

A:

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A: Here we take the substitution x-1 = u to solve this integration.

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Q: b) Calculate the following definite integral: [* (√x - 1) dx

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A: Given information: The indefinite integral is ∫cos5tsintdt Trigonometric identities used:…

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A:

Q: 10. Find the indefinite integral. Te cos 3t dt dv u = du = v =

A: Given integration is : ∫e9tcos3t dt   To find the value of integration.

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A: Given, ∫0π6sintcos2tdt  We have to evaluate the definite integral.

Q: Evaluate the definite integral. 7 cos(t/2) dt

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Q: Evaluate the indefinite integral.

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A: Consider the given indefinite integral, ∫cos5tsin tdt use the trigonometric identity, cos2x=1-sin2x…

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A: We need to evaluate the following integral. So,            ∫014cosπt2dt=4·∫01cosπt2dtLet…

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A: See attached file for a step by step explanation to find the given integral.

Q: 11. Evaluate the definite integral S" dx. x+a?

A: Topic:- definite integration