(a) Calculate S 8(t+ 2)e¬t dt. (b) Calculate 8 (3(t – 2)) (t³ – 1) dt. - - (c) Calculate S 5(t + 4) sin(3at)et dt. ,6t2

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Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t= 0

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Q: )L{sinh(7t) + (2t + 1)U (t – 1)},

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Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

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Q: (a) sec¹ (31) √tan(3t) dt

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Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: [(cos 2y) – 3x?y²] dx + [(cos 2y) – 2x(sin 2y) – 2x³y] dy = 0 %3D

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Q: Let the position at time t seconds of a particle moving in a coordinate line be given by s(t) =…

A: Formula used:

Q: Suppose w = 8x² + 2y², X = 3 cos(t) + 9 sin(t), and y = 3 cos(t) — 9 sin(t).

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Q: (b) 9-(t+1) (42t - sin t)dt

A: Given that the integral is .The objective is to evaluate the given integral.

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A: Cauchy residue theorem: If f is holomorphic function defined on simply connected open set with…

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Q: Find f. f"(8) = sin(e) + cos(e), f(0) = 5, f'(0) = 4 f(e) = 5t – sin (t) – cos(t) + 6

A: Here we have f''θ=sinθ+cosθ, f(0)=5, f'(0) = 4 fθ=?

Q: Evaluate r(2) and r(-1) for r(t) =(sin~ t, t 2, (t2 + 1)- 1 ).

A: Given:rt=sint , t2, t2+1-1

Q: f(t) = (cost, Sint, t) f'(t) = (-sint, west, 1) 1 f'(x)) = √√(-sint) ² + ((ost ) ² + 12 F(t)= -…

A: Given that Differentiate with respect to t           Therefore