Category: Integration

Question Number 28886 by abdo imad last updated on 31/Jan/18 $$find\int \frac{x}{{cos}^{2}x}dx.$$ Answered by mrW2 last updated on 01/Feb/18 $$\int \frac{x}{{cos}^{2}x}dx$$$$=\int{x}\:{d}\left(\mathrm{tan}\:{x}\right)…

Question Number 28888 by abdo imad last updated on 31/Jan/18 $$find{I}_n={\int }_0^{\pi }\frac{dx}{1+{cos}^2\left(nx\right)}withn\in N^{★}.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 94418 by niroj last updated on 18/May/20 $$1.\mathrm{F}\mathbf{ind}\mathbf{value}\mathbf{of}\mathit{\theta }\mathrm{in}\mathrm{Mean}\mathrm{Value}\mathrm{theorem}$$$$\mathrm{f}(\mathrm{x}+\mathrm{h})=\mathrm{f}\left(\mathrm{x}\right)+{\mathrm{hf}}^{{}^{\prime }}(\mathrm{x}+\theta \mathrm{h}),\mathrm{if}\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\mathrm{x}}$$$$2.\mathrm{If}\sqrt{1-{\mathrm{x}}^2}+\sqrt{1-{\mathrm{y}}^2}=\mathrm{k}(\mathrm{x}-\mathrm{y})\mathrm{prove}\mathrm{that}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\sqrt{1-{\mathrm{y}}^2}}{\sqrt{1-{\mathrm{x}}^2}}.$$$$3.\mathrm{Solve}\mathrm{the}\mathrm{differential}\mathrm{equation}:$$$$\:\:\:\mathrm{x}^{\mathrm{2}}…

Question Number 28882 by abdo imad last updated on 31/Jan/18 $$find{\int }_{-\pi }^{\pi }\frac{2dt}{2+sint+cost}.$$ Commented by abdo imad last updated on 02/Feb/18 $${let}\:{use}\:{the}\:{ch}.\:{e}^{{it}} ={z}…

Question Number 28881 by abdo imad last updated on 31/Jan/18 $$find{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{dt}{t^2+2t+2}$$ Answered by sma3l2996 last updated on 01/Feb/18 $${I}=\int_{−\infty} ^{+\infty}…