int_0^{pi /4} tan^6 x sec^2 x , dx = | vedclass

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Question

(A) माना $t = 	an x$. तब,$dt = \sec^2 x \, dx$. जब $x = 0$,तब $t = 	an(0) = 0$. जब $x = \frac{\pi}{4}$,तब $t = 	an(\frac{\pi}{4}) = 1$. इन मानों को

Vedclass · Accepted Answer

$\frac{1}{7}$

Vedclass · Answer

(A) माना $t = 	an x$. तब,$dt = \sec^2 x \, dx$. जब $x = 0$,तब $t = 	an(0) = 0$. जब $x = \frac{\pi}{4}$,तब $t = 	an(\frac{\pi}{4}) = 1$. इन मानों को समाकलन में प्रतिस्थापित करने पर: $\int_0^1 t^6 \, dt = \left[ \frac{t^7}{7} ight]_0^1 = \frac{1}{7}(1^7 - 0^7) = \frac{1}{7}$. अतः,सही विकल्प $A$ है.

$\int_0^{\pi /4} \tan^6 x \sec^2 x \, dx = $

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