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Category: Integration

let-A-n-0-pi-2-cos-n-xdx-1-calculate-A-0-A-2-and-A-3-2-calculate-A-n-interms-of-n-3-find-0-pi-2-cos-8-xdx-

Question Number 65770 by mathmax by abdo last updated on 03/Aug/19 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{0}} ,{A}_{\mathrm{2}} \:{and}\:{A}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{A}_{{n}} {interms}\:{of}\:{n} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\int_{\mathrm{0}}…

let-X-n-0-pi-4-sin-n-xdx-1-calculate-X-0-X-1-X-2-X-3-2-find-X-n-interms-of-n-3-find-the-value-of-0-pi-4-sin-8-xdx-

Question Number 65771 by mathmax by abdo last updated on 03/Aug/19 $${let}\:{X}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{{n}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{X}_{\mathrm{0}} \:,{X}_{\mathrm{1}} \:,{X}_{\mathrm{2}} ,{X}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{X}_{{n}} {interms}\:{of}\:{n} \\…

let-f-x-0-dt-t-4-x-4-with-x-gt-0-1-determine-a-explicit-form-of-f-x-2-find-also-g-x-0-dt-t-4-x-4-2-3-give-f-n-x-at-form-of-integral-4-calculate-0-

Question Number 65767 by mathmax by abdo last updated on 03/Aug/19 $${let}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{{t}^{\mathrm{4}} +{x}^{\mathrm{4}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({t}^{\mathrm{4}} \:+{x}^{\mathrm{4}} \right)^{\mathrm{2}} }…

1-1-tan-x-arctan-x-dx-

Question Number 221 by 123456 last updated on 25/Jan/15 $$\underset{−\mathrm{1}} {\overset{+\mathrm{1}} {\int}}\mathrm{tan}\:{x}\:\mathrm{arctan}\:{x}\:{dx} \\ $$ Answered by mreddy last updated on 16/Dec/14 $$\underset{−\mathrm{1}} {\overset{+\mathrm{1}} {\int}}\mathrm{tan}\:{x}\:\mathrm{arctan}\:{x}\:{dx} \\…

evaluate-f-x-dx-where-f-x-e-x-x-0-1-x-0-lt-x-1-1-x-2-1-lt-x-2-5-2-lt-x-5-5-1-x-5-2-x-gt-5-

Question Number 216 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate} \\ $$$$\underset{−\infty} {\overset{+\infty} {\int}}{f}\left({x}\right){dx} \\ $$$$\mathrm{where} \\ $$$${f}\left({x}\right)=\begin{cases}{{e}^{{x}} }&{{x}\leqslant\mathrm{0}}\\{\mathrm{1}+{x}}&{\mathrm{0}<{x}\leqslant\mathrm{1}}\\{\mathrm{1}+{x}^{\mathrm{2}} }&{\mathrm{1}<{x}\leqslant\mathrm{2}}\\{\mathrm{5}}&{\mathrm{2}<{x}\leqslant\mathrm{5}}\\{\frac{\mathrm{5}}{\mathrm{1}+\left({x}−\mathrm{5}\right)^{\mathrm{2}} }}&{{x}>\mathrm{5}}\end{cases} \\ $$ Answered by…

calculus-find-i-n-2-1-n-n-2-1-ii-n-2-1-n-n-4-1-

Question Number 131286 by mnjuly1970 last updated on 03/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:{calculus}\:…. \\ $$$$\:\:\:\:\:{find}\:::\:\:{i}::\:\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} −\mathrm{1}}=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ii}::\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{4}} −\mathrm{1}}\right)=? \\ $$$$\:\:\:\: \\…