Category: Integration

Question Number 144064 by 0731619 last updated on 21/Jun/21 Answered by MJS_new last updated on 21/Jun/21 $$\mathrm{simply}\mathrm{let}t=\tan x$$$$\Rightarrow \mathrm{answer}\mathrm{is}$$$$−\frac{{x}}{{b}^{\mathrm{2}} }+\frac{\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}{{ab}^{\mathrm{2}} }\mathrm{arctan}\:\frac{{a}\mathrm{tan}\:{x}}{\:\sqrt{{a}^{\mathrm{2}}…

Question Number 144053 by mnjuly1970 last updated on 21/Jun/21 $$$$$$\dots \dots ..Calculus\dots \dots ..$$$$\mathrm{\Omega }:=lim\frac{1}{\pi }{\int }_0^{2\pi }{\left(\underset{k=1}{\sum ^n}\frac{sin\left(kx\right)}{\sqrt{2^k}}\right)}^{2}dx=?$$$$$$ Answered…

Question Number 144042 by maryxxxx last updated on 20/Jun/21 Answered by mindispower last updated on 20/Jun/21 $$\int \frac{dx}{x^3\sqrt{1-{\left(\frac{10}{x}\right)}^2}}$$$$y=\frac{100}{x^2},y<1\Rightarrow dy=\frac{-200}{x^3}dx$$$$\Rightarrow\frac{−\mathrm{1}}{\mathrm{200}}\int\frac{{dy}}{\:\sqrt{\mathrm{1}−{y}}}{dy}=\frac{\mathrm{1}}{\mathrm{100}}\sqrt{\mathrm{1}−{y}}+{c}=\frac{\sqrt{\mathrm{1}−\frac{\mathrm{100}}{{x}^{\mathrm{2}}…

Question Number 78468 by Dah Solu Tion last updated on 17/Jan/20 $$IfF\left(x\right)={\int }_0^{arctanx}\sqrt{\frac{t^4-1}{t^4+1}dt,}find{F}^{\prime }\left(x\right).$$ Commented by mathmax by abdo last updated…

Question Number 12908 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 06/May/17 Answered by 433 last updated on 07/May/17 $${\int }_{\sqrt{2}}^2\left(\frac{x^2}{x+[x+1]}\right)dx+{\int }_2^{\sqrt{5}}\left(\frac{x^2}{x+[x+1]}\right)dx=$$$$\int_{\sqrt{\mathrm{2}}}…