Mathematics · essential
Even function over symmetric interval for JEE
The fundamental theorem of calculus, properties of definite integrals
Formula
\[f(-x)=f(x) \implies \int_{-a}^{a} f(x)\,dx=2\int_0^{a} f(x)\,dx\]
Conditions: \(f\) integrable on \([-a,a]\).
Symmetry-based evaluation.