Question
If $f^{\prime}$ is continuous on $[a, b],$ show that$$2 \int_{a}^{b} f(x) f^{\prime}(x) d x=[f(b)]^{2}-[f(a)]^{2}$$
Step 1
We can use the substitution method to solve this integral. Let's substitute $t = f(x)$, which implies that $\frac{dt}{dx} = f^{\prime}(x)$. Show more…
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