Integrals Set-2

$\displaystyle \frac{\pi}{4}-\arctan 2$

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

$\displaystyle \arctan 2-\frac{\pi}{4}$

$\displaystyle \arctan 2+\frac{\pi}{4}$

$\displaystyle\frac{\pi}{4}\ln 2$

$\displaystyle\frac{\pi}{8}\ln 2$

$\displaystyle\frac{3\pi}{16}\ln 2$

$\displaystyle\frac{\pi}{16}\ln 2$

$\displaystyle\frac{\pi}{4}$

$\displaystyle\frac{\pi}{8}$

$\displaystyle\frac{\pi}{3}$

$\displaystyle\frac{\pi}{2}$

Both Assertion and Reason are true but Reason is not the correct explanation for the Assertion.

Assertion is true and Reason is false.

Assertion is false and Reason is true.

Both Assertion and Reason are true and Reason is the correct explanation for the Assertion.

$\displaystyle\ln\!\left(\frac{m+1}{\,n+1\,}\right)$

$\displaystyle\frac{1}{2}\ln\!\left(\frac{m}{n}\right)$

$\displaystyle\ln\!\left(\frac{m}{n}\right)$

$\displaystyle\ln\!\left(\frac{m+1}{n}\right)$

$\ln 2$

$\ln\frac{3}{2}$

$\ln 3$

$\frac{1}{2}\ln\frac{3}{2}$

$\dfrac{\pi-2}{4}$

$\dfrac{\pi-3}{4}$

$\dfrac{\pi-1}{4}$

$\dfrac{\pi+1}{4}$

$1$

$\dfrac{\pi}{4}$

$\dfrac{\pi}{3}$

$\dfrac{\pi}{2}$

$\dfrac{\pi^{2}}{12}$

$\dfrac{\pi^{2}}{6}$

$\dfrac{(\ln 2)^{2}}{2}$

$\dfrac{\pi^{2}}{8}$

$\dfrac{\pi}{4}$

$1$

$2$

$\dfrac{1}{2}$