Category: Integration

Question Number 200930 by Spillover last updated on 26/Nov/23 $$If{I}_n={\int }_0^1{(1-x^4)}^{n}dxand\frac{I_n}{I_{n-1}}=\frac{\lambda n}{\lambda n+1}$$$$thenfind\lambda$$ Commented by mr W…

Question Number 200915 by Rupesh123 last updated on 26/Nov/23 Answered by Frix last updated on 26/Nov/23 $$\mathrm{Assume}$$$$\int\frac{\left({x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{5}}} }{{x}^{\frac{\mathrm{8}}{\mathrm{5}}} }{dx}=\frac{{p}\left({x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{1}\right)^{\frac{{q}}{\mathrm{5}}} }{{x}^{\frac{{r}}{\mathrm{5}}} }…

Question Number 200844 by darklord last updated on 24/Nov/23 Commented by som(math1967) last updated on 24/Nov/23 $$??$$ Commented by darklord last updated on…

Question Number 200802 by mnjuly1970 last updated on 23/Nov/23 Answered by witcher3 last updated on 23/Nov/23 $$\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\infty} \mathrm{t}^{\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{1}} \mathrm{e}^{−\mathrm{t}} \mathrm{dt},\mathrm{x}^{\mathrm{2}}…

Question Number 200748 by Rupesh123 last updated on 22/Nov/23 Answered by MM42 last updated on 22/Nov/23 $$\left.{s}=\mathrm{4}\int_{\mathrm{0}} ^{{c}} \left({c}^{\mathrm{2}} −{x}^{\mathrm{2}} \right){dx}=\mathrm{4}\left({c}^{\mathrm{2}} {x}−\frac{\mathrm{1}}{\mathrm{3}}{x}^{\mathrm{3}} \right)\right]_{\mathrm{0}} ^{{c}} \…