Teaching UP TGT Mock Test Series 2025 Mathematics Integral Calculus Properties of Definite Integrals
Let f and g be continuous functions on [0, a] such that f(x) = f(a - x) and g(x) + g(a - x)=4, then \(\int\limits_0^a {f\left( x \right)g\left( x \right)dx} \) is equal to
1
\(4\int\limits_0^a {f\left( x \right)dx} \)
2
\(2\int\limits_0^a {f\left( x \right)dx} \)
3
\( - 3\int\limits_0^a f \left( x \right)dx\)
4
\(\int\limits_0^a {f\left( x \right)dx} \)