Category: Integration

Question Number 147799 by Eric002 last updated on 23/Jul/21 $$\int \frac{\sqrt{2-x^2}+\sqrt{2+x^2}}{\sqrt{4-x^2}}dx$$ Answered by Khalmohmmad last updated on 24/Jul/21 Terms of Service…

Question Number 16703 by Tinkutara last updated on 25/Jun/17 $$\mathrm{Evaluate}:{\int }_0^{\frac{1}{2}}\frac{dx}{(1+x^2)\sqrt{1-x^2}}$$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 26/Jun/17 $${x}={tg}\varphi\Rightarrow{dx}=\left(\mathrm{1}+{tg}^{\mathrm{2}} \varphi\right){d}\varphi…

Question Number 82223 by jagoll last updated on 19/Feb/20 $$givenf\left(x\right)=f(x+\frac{\pi }{6}),\mathrm{\forall }x\in \mathbb{R}$$$$if\underset{0}{\stackrel{\frac{\pi }{6}}{\int }}f\left(x\right)dx=T$$$$then\underset{\pi }{\stackrel{\frac{7\pi }{3}}{\int }}f(x+\pi )dx=?$$ Commented by john santu last…

Question Number 147746 by 0731619 last updated on 23/Jul/21 Answered by mindispower last updated on 23/Jul/21 $$\frac{{tan}^{-}\left(x^2\right)}{{tan}^{-}\left(x\right)}<1$$$${x}\leqslant{x}^{\mathrm{2}} <\mathrm{1},\:{and}\:{using}\:{tan}^{−} \:{increasing}\:{function} \…

Question Number 82185 by jagoll last updated on 19/Feb/20 $$\int \frac{dx}{\sec x+cscx}=?$$ Commented by john santu last updated on 19/Feb/20 $$\sec x+cscx=\frac{1}{\cos x}+\frac{1}{\sin x}$$$$\frac{\sin x+\cos x}{\sin x\cos x}.$$$$\int\:\frac{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}}\:{dx}\:=\:…