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Category: Integration

L-1-2bt-t-e-bt-s-

Question Number 142285 by qaz last updated on 29/May/21 $$\mathscr{L}\left(\frac{\mathrm{1}+\mathrm{2bt}}{\:\sqrt{\mathrm{t}}}\mathrm{e}^{\mathrm{bt}} \right)\left(\mathrm{s}\right)=? \\ $$ Answered by Dwaipayan Shikari last updated on 29/May/21 $$\mathscr{L}\left({f}\left({t}\right)\right)\left({s}\right)=\int_{\mathrm{0}} ^{\infty} {f}\left({t}\right){e}^{−{st}} \:{dt}…

1-3-3-x-sin-x-2-1-x-2-x-2-cos-x-1-x-dx-

Question Number 142273 by liberty last updated on 29/May/21 $$\:\:\underset{\frac{\mathrm{1}}{\mathrm{3}}} {\overset{\mathrm{3}} {\int}}\:\frac{{x}+\mathrm{sin}\:\left({x}^{\mathrm{2}} −\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)}{{x}\left(\mathrm{2}+\mathrm{cos}\:\left({x}+\frac{\mathrm{1}}{{x}}\right)\right)}\:{dx}\:? \\ $$ Commented by abdullahoudou last updated on 29/May/21 $${u}=\mathrm{1}/{x} \\…

Question-142248

Question Number 142248 by gsk2684 last updated on 28/May/21 Commented by gsk2684 last updated on 31/May/21 $$\mathrm{let}\:\mathrm{a}>\mathrm{0}\:\mathrm{and} \\ $$$$\mathrm{D}=\left\{\left(\mathrm{x},\mathrm{y}\right)/\mathrm{0}\leq\mathrm{x}\leq\mathrm{1},\mathrm{0}\leq\mathrm{y}\leq\mathrm{3x}\right\} \\ $$$$\mathrm{consider}\:\mathrm{the}\:\mathrm{following}\:\mathrm{integral} \\ $$$$\int\underset{\mathrm{D}} {\int}\left(\mathrm{3x}+\mathrm{y}\right)\left(\mathrm{3x}−\mathrm{y}\right)^{\mathrm{a}} \mathrm{dxdy}…