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IntegrationQuestion and Answers: Page 24

Question Number 202485 Answers: 0 Comments: 3

Question Number 202448 Answers: 2 Comments: 0

Question Number 202418 Answers: 1 Comments: 0

Hard integral ∫∫∫∫∫∫∫∫∫ determinant ((a,b,c),(f,g,h),(j,k,l))dl dk dj dh dg df dc db da=

$$\mathrm{Hard}\:\mathrm{integral} \\ $$$$\int\int\int\int\int\int\int\int\int\begin{vmatrix}{{a}}&{{b}}&{{c}}\\{{f}}&{{g}}&{{h}}\\{{j}}&{{k}}&{{l}}\end{vmatrix}{dl}\:{dk}\:{dj}\:{dh}\:{dg}\:{df}\:{dc}\:{db}\:{da}= \\ $$

Question Number 202415 Answers: 2 Comments: 0

The value of ∫g′(x)f′(g(x))dx is...

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\int{g}'\left({x}\right){f}'\left({g}\left({x}\right)\right){dx}\:\mathrm{is}... \\ $$

Question Number 202406 Answers: 2 Comments: 0

Question Number 202388 Answers: 1 Comments: 0

P rove that: ∫ (dx/(b^4 +2ax^2 +c))=((tan^(−1) ((((√2)(√a)x)/( (√(c+b^4 ))))))/( (√2)(√a)(√(c+b^4 ))))+C if a∙(c+b^4 )>0

$$\:\:\boldsymbol{{P}}\:\boldsymbol{{rove}}\:\boldsymbol{{that}}:\:\:\:\:\int\:\frac{\boldsymbol{{dx}}}{\boldsymbol{{b}}^{\mathrm{4}} +\mathrm{2}\boldsymbol{{ax}}^{\mathrm{2}} +\boldsymbol{{c}}}=\frac{\boldsymbol{{tan}}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{2}}\sqrt{\boldsymbol{{a}}}\boldsymbol{{x}}}{\:\sqrt{\boldsymbol{{c}}+\boldsymbol{{b}}^{\mathrm{4}} }}\right)}{\:\sqrt{\mathrm{2}}\sqrt{\boldsymbol{{a}}}\sqrt{\boldsymbol{{c}}+\boldsymbol{{b}}^{\mathrm{4}} }}+\boldsymbol{{C}} \\ $$$$\boldsymbol{{if}}\:\:\boldsymbol{{a}}\centerdot\left(\boldsymbol{{c}}+\boldsymbol{{b}}^{\mathrm{4}} \right)>\mathrm{0} \\ $$$$ \\ $$

Question Number 202212 Answers: 1 Comments: 1

Question Number 202167 Answers: 2 Comments: 0

∫^1 _0 ∫^1 _x sin(y^2 )dydx = ¿

$$\underset{\mathrm{0}} {\int}^{\mathrm{1}} \underset{{x}} {\int}^{\mathrm{1}} {sin}\left({y}^{\mathrm{2}} \right){dydx}\:=\:¿ \\ $$

Question Number 202127 Answers: 1 Comments: 0

Question Number 202125 Answers: 1 Comments: 0

∫ ((sin(3x))/(1+sin^3 x))dx

$$\int\:\frac{\boldsymbol{{sin}}\left(\mathrm{3}\boldsymbol{{x}}\right)}{\mathrm{1}+\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{x}}}\boldsymbol{{dx}} \\ $$

Question Number 201925 Answers: 0 Comments: 2

Question Number 201982 Answers: 0 Comments: 0

Question Number 201980 Answers: 1 Comments: 0

Question Number 201817 Answers: 1 Comments: 0

Question Number 201762 Answers: 1 Comments: 0

Question Number 201727 Answers: 1 Comments: 0

∫_(π/6) ^(π/3) e^(sin x^(cos x^(tan x^(cot x^(sec x^(cosec x) ) ) ) ) ) dx

$$\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} {e}^{\mathrm{sin}\:{x}^{{c}\mathrm{os}\:{x}^{\mathrm{tan}\:{x}^{\mathrm{cot}\:{x}^{\mathrm{sec}\:{x}^{\mathrm{cosec}\:{x}} } } } } } {dx} \\ $$

Question Number 201646 Answers: 1 Comments: 0

Question Number 201644 Answers: 0 Comments: 0

Question Number 201553 Answers: 3 Comments: 0

Question Number 201548 Answers: 1 Comments: 0

Question Number 201546 Answers: 2 Comments: 4

∫Sin(Inx)dx

$$\:\:\:\int\boldsymbol{{Sin}}\left(\boldsymbol{{Inx}}\right)\boldsymbol{{dx}} \\ $$

Question Number 201510 Answers: 1 Comments: 0

Question Number 201509 Answers: 1 Comments: 0

Question Number 201452 Answers: 2 Comments: 0

Question Number 201445 Answers: 0 Comments: 0

Question Number 201347 Answers: 1 Comments: 0

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