Calculus II Integration by parts

Question

Suppose that ƒ(1)=-8, ƒ(4)=-2, ƒ'(1)=1, ƒ'(4)=-1 and ƒ'' is continuous.

Find the value of the integral from 1 to 4 ∫xƒ''(x)dx

Answer 1

plugin the number from the question you will get your final answer.

Answer 2

By the integration by parts formula we have that the requested integral equals (xf'(x) evaluated at 4) minus (xf'(x) evaluated at 1) - f(4) + f(1)=4f'(4)-f'(1)-f(4)+f(1)=4(-1)-1-(-2)+(-8)=-4-1+2-8=-5-6=-11.