1. In the following exercises, evaluate each definite integral using the Fundamental Theorem of Calculus, Part 2. (e) 2 (a) (x-3x)dx (f) x dx 99 -1 3 (b) [(x +3x-5)dx (g) [(412 – 3r ) dt 5/2 3/2 -2 3. (c) [(+2)(1-3)dt (h) dx .2 -2 3 (d) [( -9)(4-r)dt (i) 2

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Q: (b) | sin(x) – 7dx -

A: ∫0πsin(x)-7 dxLet the lower limit of integral is a and the upper limit be bSo now according to the…

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Q: Use Cayley-Hamilton theorem to find (i) the inverse of A = (ii) A

A: This question is related to matrix, we will solve it using given information.

Q: If f(x) = x√(x+3) and a=2, find (f-1)'(a). f is a one to one function

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Q: a) f(x) = 1+ Sinx b) f(x) = x² + 2x- 1 c) f(x) = 2* + 2 for all x eR for all x eR for all x eR

A: Given function are: [1] f(x) = 1 + Sinx   for all x ∈R [2] f(x) = x2 + 2x - 1  for all x ∈R [3] f(x)…