List of top Mathematics Questions on Definite Integral asked in MET

A real differentiable function \(f\) satisfies \(f(x)+f(y)+2xy=f(x+y)\). Given \(f''(0)=0\), then \[ \int_0^{\pi/2} f(\sin x)\,dx = \]
Let \( f(x) \) be a polynomial such that \( f(x) + f(1/x) = f(x)f(1/x) \), \( x > 0 \). If \( \int f(x)\,dx = g(x) + c \) and \( g(1) = \frac{4}{3} \), \( f(3) = 10 \), then \( g(3) \) is:
If \( f : \mathbb{R} \to \mathbb{R} \) is a differentiable function and \( f(3) = 6 \), then \[ \lim_{x \to 3} \frac{\displaystyle \int_{6}^{f(x)} \frac{2t \, dt}{t - 2}}{x - 3} \text{ is equal to} \]
\(\int_0^1 \sin^{-1}x \, dx\) is
\(\int_1^e \frac{\log x}{x} \, dx\) is
\(\int_{-\pi/2}^{\pi/2} |\sin x| dx\) is
\(\int_0^1 x(1-x)^{12 dx\) is equal to}
The value of \(\int_{0}^{\sqrt{\ln\left(\frac{\pi}{2}\right)}} \cos\left(e^{x^2}\right)\, 2x e^{x^2}\, dx\) is
By trapezoidal rule, approximate value of \(\int_0^6 \frac{dx}{1+x^2}\)

Evaluate \(\int \frac{1}{(x+1)\sqrt{x^2 - 1}}\) dx

\( \int_{0}^{\pi} \frac{1}{1+\sin x} \, dx \) is equal to
The value of \( \int_{0}^{1} x e^{x} \, dx \) is:
The value of \( \int_{0}^{1} x e^{x} \, dx \) is:
The value of \( \int_{0}^{1} \frac{dx}{1 + x^{2}} \) is: