Find: Q = j 0 ra In (ax) 72 Σπ j=0 1-1 Στ 1=0 dx ;0

Q: S10 e-30t sin(40t) dt

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Q: If z = In(x – y) + tan(x + y), show that Z = Z, XX

A: We have to show that given expression.

Q: 0 and f(5) /4. Is'(x) sin (f(x)) dæ Calculate 8. +1 8 8. O T 4 1 112 1/2

A: We are authorized to solve only 1 question, please repost remaining questions Definite integration

Q: 4. Evaluate + tyt - 1j+t sin at k) dt

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Q: Using Fourier sine integral, show that HART (1- cos Th) |n/ 2, for 0 T.

A: We have to show that ∫0∞1-cosπλλsinx λdλ=π2,   0<x<π0,    x>π, using Fourier sine integral.…

Q: dx b) V2+ V3x² +1

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: [-7, 1] The average value of cos (2z)e1-sin(2z) on is

A: The average value of the function f(z) on the interval a, b is  1b-a∫abf(z) dz.

Q: 2t : Evaluate the integral [ de 0 3+ cos(0)

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Q: sin 3z C:|z| = T _2 e2/z C: ]z – 1 – i| = 2 5z z? + 4' 23 C:\z| = 3 2

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Q: (t – sin t)v1 – cos t dt

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Q: Use the Fundamental Theorem of Calculus to compute In(tan(t²-1)) 12+A arctan (et) cos(t³) -π d dx…

A: By using the Fundamental Theorem of Calculus to compute  ddx∫-πx+4 lntanπt2-1arctanet-cost3 dt.

Q: Let r(t) = cos(t) i + 4 ln(t² + t)j + 5 tan¯¹(t) k. Find 7' (t).

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Q: Find 19. t sin 3t dt Jo

A: Topic:- integration  Note:- as per our guideline if more than one question uploaded than only first…

Q: 1 If the integral A = S -dx is changed using substitution t = tan then A = ... sin x-cos x 1 Jika t…

A: A =∫ 1dx/(sinx - cosx) substitute  t = tan(x/2) differentiate with x dt/dx =(sec2(x/2))/2 dx =…

Q: Let z = e* + In( y), x = sin (uv), y° = cos (uv). 2 Determine at u = 1, v= 3

A: Topic- partial derivatives

Q: Prove: L{cos at} = s2+ a?

A: We will prove the given statement.

Q: If the temperature at which a certain compound melts is a random variable with mean value 115°C and…

A: We have to solve given Questions.

Q: X Evaluate the integral sin cos -dx. 2 4 X 2 X X [sin 4 cos dx = 2 2

A: Given indefinite integral ∫sin4x2cosx2dx

Q: A particle moves so that r(t) = (3 cos t + 3t sin t)i + (3 sint – 3t cos t)j+ (2t² )k. Find the…

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Q: Show that in the interval (0,1) COS TTX = ∞ TT n=1 n 4n²-11 -sin 2nπx

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Q: T/2 / csc²x dx л/4 T/2 / (csc?x +o ´x + csc x cot x) dx T/2 csc x cot x dx

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Q: Which of the following DEs are first order linear DEs?

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Q: 1 (d) Last week, Amy walked a median of 7.5 kilometres each day. 1 kilometre = 0.6 miles The table…

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Q: Show that cos λx 2² +1 -dλ TU že 2 x ≥ 0.

A: Given: x≥0 To show:∫0∞cosxλλ2+1dλ=π2e-x.