Definite Integration - Calculus - Mathematics Previous Year Questions

$$\int\limits_0^{\pi / 2} \frac{1}{a^2 \cdot \sin ^2 x+b^2 \cdot \cos ^2 x} d x$$

$$\int\limits_{-\pi / 2}^{\pi / 2} \frac{d x}{e^{\sin x}+1}$$

$$\int_\limits{-3}^3 \cot ^{-1} x d x=$$

$$\int_\limits0^1 \sqrt{\frac{1+x}{1-x}} d x=$$

$$\int_\limits0^2\left[x^2\right] d x=$$

Find the value of \(\int_0^1 \frac{\log (1+x)}{1+x^2} d x\) is

The value of \(\int_{-1 / 2}^{1 / 2} \cos ^{-1} x d x\) is

The value of \(\int_{-\pi / 2}^{\pi / 2} \frac{\cos x}{1+e^x} d x\) is

If \(I_n=\int_0^{\frac{\pi}{4}} \tan ^n x d x\), where \(n\) is positive integer, then \(I_{10}+I_8\) is equal to

The value of \(\int_0^{4042} \frac{\sqrt{x} d x}{\sqrt{x}+\sqrt{4042-x}}\) is equal to

\(\int_0^{\pi / 2} \sqrt{\sin \theta} \cos ^3 \theta d \theta\) is equal to

If \([x]\) is the greatest integer function not greater than \(x\), then \(\int_\limits0^8[x] d x\) is equal to

\(\int_0^1 \frac{x e^x}{(2+x)^3} d x\) is equal to

Evaluate \(\int_\limits2^3 x^2 d x\) as the limit of a sum