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Category: Integration

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}…

x-5-x-3-1-1-3-dx-

Question Number 11149 by suci last updated on 14/Mar/17 $$\int{x}^{\mathrm{5}} \:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx}=…??? \\ $$ Answered by ajfour last updated on 14/Mar/17 $$\:\frac{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{7}/\mathrm{3}} }{\mathrm{7}}−\frac{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{4}/\mathrm{3}}…

sin-3-1-2x-dx-

Question Number 11146 by suci last updated on 14/Mar/17 $$\int{sin}^{\mathrm{3}} \left(\mathrm{1}+\mathrm{2}{x}\right){dx}=….??? \\ $$ Answered by ajfour last updated on 14/Mar/17 $$=\:−\frac{\mathrm{3}}{\mathrm{8}}\mathrm{cos}\:\left(\mathrm{2}{x}+\mathrm{1}\right)+\frac{\mathrm{1}}{\mathrm{24}}\mathrm{cos}\:\left(\mathrm{6}{x}+\mathrm{3}\right)+{C} \\ $$ Commented by…