Let f be twice differentiable with f(0)=12, f(3)=9, and f '(3)=4.Evaluate the integral upper limit 3 and lower integral 0 xf'' (x)dx

Answer 1

using integration by parts,
∫xf" dx = xf' - ∫f' dx = (xf' - f)[0,3]
= [3f'(3)-f(3)]-[0f'(0)-f(0)]
= (3*4-9)-(0-12)
= 3+12 = 15

Answer 2

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Answer 3

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Answer 4

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