Asked by Jake
Let f be twice differentiable with f(0)=3 f(1)=2, and f′(1)=4. Evaluate the integral ∫[1,0] xf″(x)dx
Answers
Answered by
oobleck
use integration by parts
u = x, dv = f"(x) dx
du = dx, v = f'(x)
∫xf″(x) dx = xf'(x) - ∫f'(x) dx = xf'(x) - f(x)
Now evaluate at the limits and subtract.
u = x, dv = f"(x) dx
du = dx, v = f'(x)
∫xf″(x) dx = xf'(x) - ∫f'(x) dx = xf'(x) - f(x)
Now evaluate at the limits and subtract.
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