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IntegrationQuestion and Answers: Page 158
Question Number 102330 Answers: 0 Comments: 0
$${Do}\:{this}\:{integration}\left({please}\:{do}\:{it}\:{step}\:{by}\:{step}\:{and}\:{write}\:{the}\:{used}\:{formula}\right) \\ $$$$\int\frac{\mathrm{1}}{\mathrm{2}}\left({sin}\:{x}\right)\left({e}^{{sin}\:{x}} \right){dx} \\ $$
Question Number 102275 Answers: 0 Comments: 2
$$\int_{\mathrm{1}} ^{\mathrm{2}} \:\boldsymbol{{ln}}\left(\frac{\boldsymbol{{x}}^{\mathrm{4}} \:+\:\mathrm{4}}{\boldsymbol{{x}}^{\mathrm{2}} \:+\:\mathrm{4}}\right)\frac{\boldsymbol{{dx}}}{\boldsymbol{{x}}} \\ $$
Question Number 102233 Answers: 1 Comments: 0
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{under}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\sqrt{\mathrm{a}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{included}\:\mathrm{between}\:\mathrm{the}\:\mathrm{lines}\:\mathrm{x}=\mathrm{0}\:\mathrm{and}\:\mathrm{x}=\mathrm{4} \\ $$$$ \\ $$$$\mathrm{plz}\:\mathrm{help}..... \\ $$
Question Number 102198 Answers: 2 Comments: 0
$$\int\frac{{x}}{{sin}^{\mathrm{2}} {x}−\mathrm{3}}{dx}=? \\ $$
Question Number 102195 Answers: 2 Comments: 0
$$\int{sinx}\:{d}\left({sinx}\right)=? \\ $$
Question Number 102169 Answers: 5 Comments: 0
$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{\mathrm{3}/\mathrm{2}} \:\sqrt{\mathrm{1}−{x}}\:{dx}\:? \\ $$
Question Number 102165 Answers: 2 Comments: 0
$$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$
Question Number 102163 Answers: 1 Comments: 0
$$\mathrm{solve}\:\:\mathrm{y}^{''} \:−\mathrm{2xy}^{'} \:\:=\mathrm{xe}^{−\mathrm{x}^{\mathrm{2}} } \\ $$
Question Number 102161 Answers: 0 Comments: 0
$$\mathrm{find}\:\int\:\frac{\mathrm{x}\sqrt{\mathrm{x}−\mathrm{1}}−\left(\mathrm{x}−\mathrm{1}\right)\sqrt{\mathrm{x}}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}}−\mathrm{x}\sqrt{\mathrm{x}+\mathrm{1}}}\:\mathrm{dx} \\ $$
Question Number 102160 Answers: 0 Comments: 0
$$\left.\mathrm{1}\right)\:\mathrm{let}\:\mathrm{a}<\mathrm{1}\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{cos}\theta\mathrm{d}\theta}{\left(\mathrm{a}^{\mathrm{2}} −\mathrm{2acos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{\mathrm{cos}\theta}{\left(\mathrm{4}−\mathrm{2}\sqrt{\mathrm{3}}\mathrm{cos}\theta\right)^{\mathrm{2}} }\mathrm{d}\theta \\ $$$$ \\ $$
Question Number 102158 Answers: 1 Comments: 0
$$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{9}\right)^{\mathrm{2}} } \\ $$
Question Number 102159 Answers: 0 Comments: 0
$$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} \left(\:\mathrm{2x}^{\mathrm{2}} \:+\mathrm{5}\right)} \\ $$
Question Number 102138 Answers: 0 Comments: 0
$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\sqrt{{y}}} ^{\mathrm{0}} \sqrt{{x}^{\mathrm{3}} +\mathrm{1}+{ax}^{\mathrm{2}} +{bx}+{c}}\:\:{dx}\:{dy} \\ $$
Question Number 102128 Answers: 4 Comments: 0
$$\:\int\frac{{x}+\mathrm{1}}{\sqrt{{x}}\:+\mathrm{1}}{dx}=? \\ $$
Question Number 102121 Answers: 3 Comments: 1
$$\int_{−\infty} ^{\infty} \frac{{sin}\left({x}+\frac{\pi}{\mathrm{2}}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:{By}\:{real}\:{analysis} \\ $$
Question Number 102115 Answers: 3 Comments: 3
$$\Gamma\left({s}\right)\zeta\left({s}\right)=\int_{\mathrm{0}} ^{\infty} \frac{{x}^{{s}−\mathrm{1}} }{{e}^{{x}} +\mathrm{1}}{dx}\:\:\left({Prove}\:{that}\right) \\ $$$${And}\:{prove}\:\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+....\infty=−\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$ \\ $$
Question Number 102127 Answers: 1 Comments: 0
$$\int_{\mathrm{0}} ^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} {dx}=? \\ $$$$\:{and}\:{write}\:{the}\:{furmollah} \\ $$
Question Number 102099 Answers: 1 Comments: 0
$$\int{sinx}\:\centerdot\:{cosx}\:\centerdot{cos}\mathrm{2}{x}\:\centerdot\:{cos}\mathrm{4}{x}\:{dx}=? \\ $$
Question Number 102097 Answers: 0 Comments: 2
$$\int\frac{{cos}^{\mathrm{2}} {x}\:−{cos}^{\mathrm{2}} {x}}{{cosx}−{cosx}}{dx}=? \\ $$
Question Number 102065 Answers: 1 Comments: 0
$$\int\:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}}{\left(\mathrm{1}−\mathrm{x}\right)\sqrt{\mathrm{x}}}\:? \\ $$
Question Number 102064 Answers: 1 Comments: 0
$$\int\:\frac{\mathrm{sin}\:\mathrm{3x}}{\mathrm{cos}\:\mathrm{5x}.\:\mathrm{cos}\:\mathrm{2x}}\:\mathrm{dx}\:? \\ $$
Question Number 102043 Answers: 0 Comments: 1
$$\int{e}^{\sqrt{{ax}+{b}}} {dx} \\ $$
Question Number 102001 Answers: 2 Comments: 0
$${evaluate}\:\int\mathrm{cos}\:^{\mathrm{3}} {x}\mathrm{sin}\:^{\mathrm{3}} {xdx}. \\ $$
Question Number 101985 Answers: 1 Comments: 0
$$\int\:\frac{\mathrm{3x}^{\mathrm{5}} \:−\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{9x}^{\mathrm{3}} \:−\:\mathrm{12x}^{\mathrm{2}} \:−\:\mathrm{2x}\:\:+\:\:\mathrm{1}}{\left(\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$
Question Number 102058 Answers: 1 Comments: 0
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sin}\left({logx}\right)}{{logx}}{dx} \\ $$
Question Number 102183 Answers: 4 Comments: 0
$$\int\:\frac{\mathrm{cos}\:\theta}{\mathrm{sin}\:\theta−\mathrm{cos}\:\theta}\:{d}\theta\:? \\ $$
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