Mathematics · essential
Pairing property using symmetry for JEE
The fundamental theorem of calculus, properties of definite integrals
Formula
\[\int_a^b f(x)\,dx=\frac{1}{2}\int_a^b \big(f(x)+f(a+b-x)\big)\,dx\]
Conditions: \(f\) integrable on \([a,b]\).
Transforming hard integrands into simpler symmetric forms.