Definite Integration - Calculus - Mathematics Previous Year Questions

$a$ is even number and $b$ is odd number

$a$ is odd number and $b$ is even number

Both $a$ and $b$ are even numbers

Both $a$ and $b$ are odd numbers

$e^2-1$

$e^2+1$

$2 e^2-2$

$2 e^2+1$

$\frac{\pi^2-2}{8}$

$\frac{\pi(\pi-2)}{8}$

$\frac{\pi-2}{8}$

$\frac{\pi+2}{8}$

$\frac{3 \pi}{128}$

$\frac{9 \pi}{32}$

$\frac{9 \pi}{64}$

$\frac{3 \pi}{64}$

$\frac{\pi}{8} \log 2$

$-\frac{\pi}{2} \log 2$

$-\frac{\pi}{4} \log 2$

$2 \pi \log 2$

$\frac{8 \sqrt{2}}{3}-3$

$\frac{16 \sqrt{2}}{3}+12$

$\frac{16 \sqrt{2}}{3}-3$

$\frac{8 \sqrt{2}}{3}+12$

$\log \left(\frac{7}{3}\right)$

$\frac{1}{4} \log \left(\frac{7}{3}\right)$

$\frac{1}{4} \log 7$

$\log 7$

$5+\sqrt{2}+\sqrt{3}$

$5+\sqrt{2}-\sqrt{3}$

$5-\sqrt{2}-\sqrt{3}$

$5-\sqrt{2}+\sqrt{3}$

$\frac{\pi}{6 \sqrt{5}}$

$\frac{\pi}{6}$

$\frac{\pi}{3}$

$\frac{\pi}{3 \sqrt{5}}$

$\tan ^{-1}\left(\frac{4}{5}\right)$

$2 \tan ^{-1}\left(\frac{3}{5}\right)$

$\frac{1}{8} \tan ^{-1}\left(\frac{8}{9}\right)$

$\frac{1}{4} \tan ^{-1}\left(\frac{7}{8}\right)$

$\frac{(-1)^n}{n-1}$

$\frac{(-1)^n}{2 n+1}$

$\frac{(-1)^{n+1}}{2 n-1}$

$\frac{(-1)^{n+1}}{n+1}$

$\int_0^1 \log x d x$

$\int_0^1 x \log x d x$

$\int_0^1(x+1) \log (x+1) d x$

$\int_0^1 \log (1+x) d x$

0

$\frac{1}{2} \log (2-\sqrt{3})$

$\frac{1}{2} \log (2+\sqrt{3})$

$\frac{1}{2} \log (2 \sqrt{3}-3)$

$\frac{81 \pi}{8}$

$\frac{9 \pi}{2}$

$\pi$

$\frac{\pi}{10}$