(15) Determine whether each integral is convergent or divergent. Evaluate those that are convergent. a) ₂ (0.dt b) ²e-tdt cos Bdß c) d) ƒ‰(7 – z³)dz e) 1 2z-5 dz [caution]

Q: (1) Evaluate or determine the definite integral: •5п a) | sint|dt, b) ₁dt, c) fe-tdt.

A:

Q: Evaluate the improper integral or show that it diverges: 00 1 :- sin (x)

A: solve improper integral by using comparison test

Q: Ss (2ava2 + 2) dæ dx r+1 vi) đt 64 Jo (sin 2x + cos 2x) dz

A: Firstly let's recall few basic integration formule.

Q: 2. Evaluate each integral below with the initial condition f(0) 2. T

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Q: 1 1 dx 1) Evaluate the integral sinh r

A: Given that ∫0∞1x-1sinhxdxx Let  L=∫0∞1x-1sinhxdxx then…

Q: 2. Evaluate the definte integral S 2 ln 3 xe -x²/2 dx.

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Q: P4. Find the following integral using integration by parts: sin ¹(4x) dx cos(In x) dx (3x + 5)…

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Q: Evaluate  integral.

A: Let the given integral function be  ₀∫⁵(x4y+y)dx  First we have to separate into two integral terms…

Q: 15. I se sec 3t tan 3t dt 17. f cos (1 + 5t) dt S

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Q: 1- x dx 21 y =

A: We solve the given integral using Trigonometry substitutions method.

Q: (2) /: (2) 5te dt (1) dx 5+e*

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Q: Use integration by parts to find L[cos t]. Do not use et.

A: Laplace transform

Q: T 7.2) [(sin x) dx 0

A: The given integral is

Q: Calculate the integral of x(1+ 3x)° dx .

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Q: Question 12 > x8 dx (29 + 7)? The integral is divergent.

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Q: de Use contour integration to evaluate the real definite integral 17- 8сos(®

A: