Techniques of Integration

Question

If g(1)=5, g(5)=7, and ∫₁⁵ g(x)dx=−6, evaluate the integral ∫₁⁵ xg′(x)dx.

Answer 1

Answer 2

Integration by parts gives the desired definite integral as

g x |₁⁵ - ∫₁⁵ g(x) dx

Plugging in gives 36