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Category: Integration

Given-a-b-x-2-3x-x-3-dx-11-2-where-a-lt-3-lt-b-a-2b-8-Find-a-b-x-dx-

Question Number 132463 by EDWIN88 last updated on 14/Feb/21 $$\:\mathrm{Given}\:\int_{{a}} ^{\:{b}} \:\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}}{\mid{x}−\mathrm{3}\mid}\:\mathrm{dx}\:=\:\frac{\mathrm{11}}{\mathrm{2}}\:\mathrm{where}\:\begin{cases}{{a}<\mathrm{3}<{b}}\\{{a}+\mathrm{2}{b}=\mathrm{8}}\end{cases} \\ $$$$\:\mathrm{Find}\:\int_{{a}} ^{{b}} \:\mid{x}\mid\:\mathrm{dx}.\: \\ $$ Answered by bemath last updated on…

Evaluate-the-following-integral-I-pi-4-pi-2-cos2x-sin2x-ln-cosx-sinx-dx-

Question Number 1350 by 112358 last updated on 24/Jul/15 $${Evaluate}\:{the}\:{following}\:{integral}: \\ $$$${I}=\int_{\pi/\mathrm{4}} ^{\:\pi/\mathrm{2}} \left({cos}\mathrm{2}{x}+{sin}\mathrm{2}{x}\right){ln}\left({cosx}+{sinx}\right)\:{dx} \\ $$ Commented by prakash jain last updated on 25/Jul/15 $$\int\mathrm{sin}\:\mathrm{2}{x}\mathrm{ln}\:\left(\mathrm{cos}\:{x}+\mathrm{sin}\:{x}\right){dx}…

let-x-gt-0-and-f-x-1-2-t-1-t-2-2xt-1-dt-1-find-a-explicit-form-of-f-x-2-determine-also-g-x-1-2-t-2-t-t-2-2xt-1-dt-3-find-the-value-of-integrals-1-2-t-1-t-2-t-1-dt

Question Number 66816 by mathmax by abdo last updated on 20/Aug/19 $${let}\:{x}>\mathrm{0}\:{and}\:{f}\left({x}\right)=\int_{\mathrm{1}} ^{\mathrm{2}} \left({t}+\mathrm{1}\right)\sqrt{{t}^{\mathrm{2}} −\mathrm{2}{xt}−\mathrm{1}}{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{t}^{\mathrm{2}} \:+{t}}{\:\sqrt{{t}^{\mathrm{2}} −\mathrm{2}{xt}−\mathrm{1}}}{dt} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:{integrals}\:\:\int_{\mathrm{1}}…

Let-consider-an-integer-serie-a-n-x-n-given-by-a-n-H-n-k-1-n-1-k-1-Find-out-the-largest-domain-D-of-convergence-of-that-integer-serie-2-x-D-explicit-the-sum-S-x-of-the-a-n-x-n

Question Number 66814 by ~ À ® @ 237 ~ last updated on 20/Aug/19 $${Let}\:{consider}\:{an}\:{integer}\:{serie}\:\left\{{a}_{{n}} {x}^{{n}} \right\}\:{given}\:{by}\:\:{a}_{{n}} \:=\:{H}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}\: \\ $$$$\left.\mathrm{1}\right)\:{Find}\:{out}\:{the}\:{largest}\:{domain}\:{D}\:{of}\:{convergence}\:{of}\:{that}\:{integer}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:\forall\:{x}\in{D}\:\:,\:{explicit}\:{the}\:{sum}\:{S}\left({x}\right)\:{of}\:{the}\:\left\{{a}_{{n}}…

let-f-x-0-2-x-t-2-dt-with-x-0-1-calculate-f-x-2-calculate-g-x-0-2-dt-x-t-2-3-find-the-value-of-0-2-4-t-2-dt-and-0-2-dt-3-t-2-4-give-g-x-at-form-of-i

Question Number 66801 by mathmax by abdo last updated on 19/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}} \sqrt{{x}+{t}^{\mathrm{2}} }{dt}\:\:\:{with}\:{x}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}} \:\frac{{dt}}{\:\sqrt{{x}+{t}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\left[{of}\:\int_{\mathrm{0}} ^{\mathrm{2}}…

very-nice-integral-4x-3-4x-2-4x-3-x-2-1-x-2-x-1-2-dx-

Question Number 132333 by liberty last updated on 13/Feb/21 $$\:\mathrm{very}\:\mathrm{nice}\:\mathrm{integral} \\ $$$$\int\:\frac{\mathrm{4x}^{\mathrm{3}} +\mathrm{4x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{3}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx}? \\ $$$$ \\ $$ Answered by EDWIN88 last…