Mathematics

The value of $$\displaystyle\int\limits_{0}^{\frac{\pi}{4}} \tan^2 \theta\  d\theta=$$


ANSWER

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


SOLUTION
Now,
$$\displaystyle\int\limits_{0}^{\frac{\pi}{4}} \tan^2 \theta\  d\theta$$
$$=\displaystyle\int\limits_{0}^{\frac{\pi}{4}} (\sec^2 \theta-1)\  d\theta$$ [ Since $$\sec^2 \theta-\tan^2 \theta=1$$]
$$=\left[\tan \theta-\theta\right]_0^{\frac{\pi}{4}}$$
$$=1-\dfrac{\pi}{4}$$.
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Single Correct Medium Published on 17th 09, 2020
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