Mathematics

Solve $$\int _{0}^{\pi} x\sec{x}\tan{x}dx$$


ANSWER

$$-\pi$$


SOLUTION
$$\displaystyle\int_{0}^{\pi}x\sec x\tan x\ dx$$
$$=x\sec \displaystyle\int_{0}^{\pi}-\int_{0}^{\pi}\sec x\ dx$$
$$=-\pi-[\ln |\sec x+\tan x|]_{0}^{\pi}$$
$$=-\pi-\ln |-1+0|+\ln |1+0|$$
$$=-\pi$$
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Single Correct Medium Published on 17th 09, 2020
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