If f' is continuous on [a,b], show that

Question

2∫_a^b f(x)f'(x)dx=[f(b)]²-[f(a)]²

Answer 1

If f' is continuous on [a,b], show that:
2∫a b f(x) f'(x) dx = [f(b)]2 - [f(a)]2
3 hours ago | Jay from Oakland, CA |
Integral Calculus, Calculus
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Answer: Note that by the Chain Rule:

d/dx f2(x) = 2f(x)f'(x)

Thus the identity

2∫ab f(x) f'(x) dx =f2(b) - f2(a).
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THIS IS A CUT-AND-PASTE of answer (by another tutor) sent to same question yesterday.