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 \[ \int_0^{\pi/2} f(\sin x)\,dx = \]

If \( f : \mathbb{R} \to \mathbb{R} \) is a differentiable function and \( f(3) = 6 \), then \[ \lim_{x \to 3} \frac{\displaystyle \int_{6}^{f(x)} \frac{2t \, dt}{t - 2}}{x - 3} \text{ is equal to} \]

The value of \( \lim_{x \to 0} \frac{\int_0^{x^2} \sec^2 t \, dt}{x \sin x} \) is

\(\int_0^1 \sin^{-1}x \, dx\) 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}

By trapezoidal rule, approximate value of \(\int_0^6 \frac{dx}{1+x^2}\)

The value of \(\int \frac{\sin x + \cos x}{3 + \sin 2x} dx\) is

The value of \(\int_0^\pi |\sin 3\theta| \, d\theta\) is

Evaluate \( \int_{0}^{\frac{3\pi}{2}} \sin\left( \left\lfloor \frac{2x}{\pi} \right\rfloor \right) dx \), where \( \lfloor \cdot \rfloor \) denotes the greatest integer function.

Evaluate \( \int_{1/n}^{(n-1)/n} \frac{\sqrt{x}}{\sqrt{a-x} + \sqrt{x}} \, dx \).

\(y = \int_{1/8}^{\sin^2 x} \sin^{-1}\sqrt{t} dt + \int_{1/8}^{\cos^2 x} \cos^{-1}\sqrt{t} dt, 0 \leq x \leq \pi/2\)

The value of \(x\) in the expression \((x + x^{\log_{10}x})^5\), if the third term in the expansion is 1,000,000, is

The limit \( \lim_{n \to \infty} \left[ \sec^2 \frac{\pi}{4n} + \sec^2 \frac{2\pi}{4n} + \dots + \sec^2 \frac{n\pi}{4n} \right] \) is equal to

The value of \[ \int_0^{\frac{\pi}{2}} | \sin x - \cos x | dx \] is:

\( \int_{0}^{\pi} \frac{1}{1+\sin x} \, dx \) 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: