Category: Integration

Question Number 86428 by jagoll last updated on 28/Mar/20 $$\int \frac{\mathrm{dx}}{\mathrm{a}\cos \mathrm{x}+\mathrm{b}\sin \mathrm{x}}?$$ Commented by jagoll last updated on 28/Mar/20 $$\mathrm{standard}\mathrm{solving}$$$$\mathrm{a}\cos \mathrm{x}+\mathrm{b}\sin \mathrm{x}=\mathrm{k}\cos (\mathrm{x}-\theta )$$$$\int\:\frac{\mathrm{dx}}{\mathrm{k}\:\mathrm{cos}\:\left(\mathrm{x}−\theta\right)}\:=\:\frac{\mathrm{1}}{\mathrm{k}}\int\:\mathrm{sec}\:\left(\mathrm{x}−\theta\right)\:\mathrm{dx} \…

Question Number 151951 by mnjuly1970 last updated on 24/Aug/21 $$$$$$nice\dots mathematics$$$$\mathrm{S}:=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{\zeta \left(2n\right)}{n.{16}^n}=?\dots \dots \mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◼"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fc.svg">}$$$$$$ Commented by Tawa11 last…

Question Number 86407 by Power last updated on 28/Mar/20 Commented by mathmax by abdo last updated on 28/Mar/20 $$A=\int \sqrt{(x-a)(b-x})dx\Rightarrow A=\int \sqrt{x-a}\sqrt{b-x}dxchsngement$$$$\sqrt{x-a}=tgivex-a=t^2\Rightarrow$$$${A}\:=\int\:\:{t}\sqrt{{b}−\left({a}+{t}^{\mathrm{2}} \right)}\left(\mathrm{2}{t}\right){dt}\:=\mathrm{2}\:\int\:{t}^{\mathrm{2}}…

Question Number 86399 by Power last updated on 28/Mar/20 Commented by Prithwish Sen 1 last updated on 28/Mar/20 $$\mathrm{put}\mathrm{x}={2\mathrm{asin}}^2\mathrm{t}$$$$\mathrm{and}\mathrm{simplify}.$$ Commented…

Question Number 20857 by Joel577 last updated on 05/Sep/17 $$\int \sqrt{\sin x}+\sqrt{\cos x}dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com