Find value of integral | Mathematics | Page 1

austere crystal Oct 20, 2022, 8:42 PM

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crimson dagger Oct 20, 2022, 8:51 PM

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Hint: let $u=\sqrt{x}$

plucky leafBOT Oct 20, 2022, 8:51 PM

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Amer

austere crystal Oct 20, 2022, 9:09 PM

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Well yeah I know how to solve it but it takes like 20 mins to solve it

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In the exam i have 5 mins

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I used this

crimson dagger Oct 20, 2022, 9:38 PM

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Ok let me try it $\int 2u\sqrt{u^2+u} ; du$

plucky leafBOT Oct 20, 2022, 9:38 PM

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Amer

crimson dagger Oct 20, 2022, 9:41 PM

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Ok another $\int \sqrt{x}\sqrt{1+\frac1{\sqrt{x}}}$

plucky leafBOT Oct 20, 2022, 9:41 PM

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Amer

crimson dagger Oct 20, 2022, 9:42 PM

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Set $u=1+1/\sqrt{x}$ then $dx=-2x^{3/2}$

plucky leafBOT Oct 20, 2022, 9:45 PM

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Amer

austere crystal Oct 21, 2022, 7:42 AM

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crimson dagger Set $u=1+1/\sqrt{x}$ then $dx=-2x^{3/2}$

Ok and

crimson dagger Oct 21, 2022, 10:27 AM

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The first sub $(u+\frac12)\sqrt{(u+\frac12)^2-\frac14}-\frac12\sqrt{(u+\frac12)^2-\frac14}du$

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The first integral the outside is the derivative of the inside

plucky leafBOT Oct 21, 2022, 10:30 AM

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Amer

crimson dagger Oct 21, 2022, 10:33 AM

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The second integral we use $\sec w=2(u+\frac12)$ so the sqrt will be just tan w

plucky leafBOT Oct 21, 2022, 10:33 AM

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Amer

#Find value of integral