Category: Integration

Question Number 118436 by bramlexs22 last updated on 17/Oct/20 $$\int \cos {}^4\left(x\right)\cos {}^4\left(2x\right)dx$$ Answered by benjo_mathlover last updated on 17/Oct/20 $$\left(1\right)\cos {}^4\left(x\right)={(\frac{1}{2}+\frac{1}{2}\cos \left(2x\right))}^2$$$$\:\:=\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\left(\mathrm{2}{x}\right)+\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\left(\mathrm{4}{x}\right)\right)…

Question Number 52900 by MJS last updated on 15/Jan/19 $$\underset{0}{\stackrel{\frac{\pi }{2}}{\int }}\sin x\sqrt{\sin 2x}dx=?$$$$\underset{-\frac{\pi }{4}}{\stackrel{\frac{\pi }{4}}{\int }}\cos x\sqrt{\cos 2x}dx=?$$ Answered by tanmay.chaudhury50@gmail.com last updated on 15/Jan/19…

Question Number 52893 by dwdkswd last updated on 14/Jan/19 $$\int \sin x\times \cos xdx$$ Answered by MJS last updated on 14/Jan/19 $$\int \sin x\cos xdx=\frac{1}{2}\int \sin 2xdx=-\frac{1}{4}\cos 2x+C=$$$$=\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{\mathrm{2}} \:{x}\:+{C}=−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{\mathrm{2}} \:{x}\:+{C} \…

Question Number 118395 by TANMAY PANACEA last updated on 17/Oct/20 $${\int }_a^b\frac{f\left(x\right)}{f\left(x\right)+f(a+b-x)}dx$$ Commented by Dwaipayan Shikari last updated on 17/Oct/20 $$\frac{{b}−{a}}{\mathrm{2}} \…

Question Number 183879 by Michaelfaraday last updated on 31/Dec/22 Terms of Service Privacy Policy Contact: info@tinkutara.com