Category: Integration

Question Number 46182 by Meritguide1234 last updated on 22/Oct/18 Commented by maxmathsup by imad last updated on 22/Oct/18 $$\:{we}\:{have}\:\mathrm{1}−{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} −….=\sum_{{n}=\mathrm{0}} ^{\infty} \left(−{x}^{\mathrm{2}} \right)^{{n}} \:=\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}}…

Question Number 177241 by peter frank last updated on 02/Oct/22 $$\int \frac{\sin \mathrm{x}}{\sin (\mathrm{x}-\mathrm{a})}\mathrm{dx}$$ Answered by cortano1 last updated on 02/Oct/22 $$\Rightarrow \mathrm{x}-\mathrm{a}=\mathrm{y};\Rightarrow \mathrm{dx}=\mathrm{dy}$$$$\mathrm{C}=\int \frac{\sin (\mathrm{a}+\mathrm{y})}{\sin \mathrm{y}}\mathrm{dy}=\int (\cos \mathrm{a}+\sin \mathrm{a}\frac{\cos \mathrm{y}}{\sin \mathrm{y}})\mathrm{dy}$$$$\mathrm{C}=\:\left(\mathrm{x}−\mathrm{a}\right)\mathrm{cos}\:\mathrm{a}+\mathrm{sin}\:\mathrm{a}\:\int\:\frac{\mathrm{d}\left(\mathrm{sin}\:\mathrm{y}\right)}{\mathrm{sin}\:\mathrm{y}}\:…

Question Number 177242 by peter frank last updated on 02/Oct/22 $$$$$$\int \frac{{3\mathrm{x}}^{16}+{5\mathrm{x}}^{14}}{{({\mathrm{x}}^5+{\mathrm{x}}^2+1)}^4}\mathrm{dx}$$$$$$ Answered by som(math1967)…

Question Number 46129 by Necxx last updated on 21/Oct/18 Commented by Meritguide1234 last updated on 21/Oct/18 $$putx=tan\theta$$$${\int }_0^{\pi /4}log(1+tan\theta )d\theta$$$$usef(a-x)\to f\left(x\right)$$$${I}=\frac{\pi}{\mathrm{8}}{log}\mathrm{2}…

Question Number 46103 by rahul 19 last updated on 21/Oct/18 $$Findtheareaenclosedbetweencurves$$$$y^2(2a-x)=x^{3}andlinex=2abovethe$$$$x-axis?$$$$Graphingcalculatorsarenotallowed..$$ Commented by rahul 19…