CUET Mathematics 2025 15 May Shift 2 PYQs

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

$\int \frac{(x^4 - x)^{1/4}}{x^5} dx$ is equal to

The value of $\int \left\{ \frac{1}{\log_e x} - \frac{1}{(\log_e x)^2} \right\} dx$ is