Question
Let $f:[-a, a] \rightarrow \mathbb{R}$ be continuous and even $(f(-x)=$ $f(x)$ ). Show that$$\int_{-a}^{a} f(x) d x=2 \int_{0}^{a} f(x) d x$$
Step 1
An even function is a function that satisfies the condition $f(-x) = f(x)$ for all $x$ in the domain of $f$. This means that the graph of an even function is symmetric with respect to the y-axis. Show more…
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