Question

High school math. Prove that:

Answer 1

\[2\int\limits_{a}^{b}f(x) f \prime(x)dx= (f(b))^{2}-(f(a))^{2}\]

Answer 2

Any help would be appreciated

Answer 3

my first impulse would be the u - sub
\(u=f(x)\)

Answer 4

should work exactly
you good from there?

Answer 5

So the left hand-side becomes: \[2\int\limits_{f(a)}^{f(b)}u \times u \prime du \] right?