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Category: Integration

Question-108429

Question Number 108429 by Rasikh last updated on 16/Aug/20 Answered by Sarah85 last updated on 17/Aug/20 $$\int\mathrm{e}^{{x}^{\mathrm{2}} } {dx}=\frac{\sqrt{\pi}}{\mathrm{2}}\int\frac{\mathrm{2e}^{{x}^{\mathrm{2}} } }{\:\sqrt{\pi}}{dx}=\frac{\sqrt{\pi}}{\mathrm{2}}\mathrm{erfi}\:\left({x}\right)\:+{C} \\ $$ Commented by…

let-0-lt-x-lt-1-and-x-0-t-x-1-e-t-dt-1-prove-that-x-1-x-pi-sin-pix-compliments-formulae-2-calculate-n-and-n-1-2-with-n-from-N-

Question Number 42870 by maxmathsup by imad last updated on 03/Sep/18 $${let}\:\mathrm{0}<{x}<\mathrm{1}\:\:{and}\:\Gamma\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\: \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\Gamma\left({x}\right).\Gamma\left(\mathrm{1}−{x}\right)\:=\frac{\pi}{{sin}\left(\pi{x}\right)}\:\:\:\left({compliments}\:{formulae}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\Gamma\left({n}\right)\:{and}\:\Gamma\left({n}+\frac{\mathrm{1}}{\mathrm{2}}\right)\:{with}\:{n}\:{from}\:{N}. \\ $$ Terms of Service…

find-the-value-of-b-so-that-the-line-y-b-divides-the-region-bound-by-the-graphs-of-the-two-functinos-into-two-regions-of-equal-area-f-x-9-x-2-and-g-x-0-

Question Number 173908 by ali009 last updated on 20/Jul/22 $${find}\:{the}\:{value}\:{of}\:{b}\:{so}\:{that}\:{the}\:{line}\:{y}={b} \\ $$$${divides}\:{the}\:{region}\:{bound}\:{by}\:{the}\:{graphs}\:{of} \\ $$$${the}\:{two}\:{functinos}\:,\:{into}\:{two}\:{regions}\:{of}\:{equal} \\ $$$${area}. \\ $$$${f}\left({x}\right)=\mathrm{9}−{x}^{\mathrm{2}} \:{and}\:{g}\left({x}\right)=\mathrm{0} \\ $$ Commented by mr W…