CUET Mathematics 2025 22 May Shift 2 PYQs

If $f(a-x) = f(x)$, then $\int_0^a xf(x)dx$ is equal to

The value of which of the following integrals is zero?

(A) $\int_0^1 x dx$

(B) $\int_{-1}^1 x dx$

(C) $\int_{-1}^1 x^2 dx$

(D) $\int_0^1 \log\left(\frac{x}{1-x}\right) dx$

Choose the correct answer from the options given below:

If $f(x)$ and $g(x)$ are continuous functions in [a, a] such that $f(x) = f(a - x)$ and $g(x) + g(a - x) = a$ then $\int_{0}^{a} f(x)g(x)dx =$