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Evaluate the integral.$\int_{0}^{a} \frac{d x}{\left(a^{2}+x^{2}\right)^{3 / 2}}, \quad a>0$

$\frac{1}{\sqrt{2} a^{2}}$

Calculus 2 / BC

Chapter 6

TECHNIQUES OF INTEGRATION

Section 2

Trigonometric Integrals and Substitutions

Integration Techniques

Improper Integrals

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Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

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Evaluate the integral.…

01:07

Evaluate the definite inte…

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$$\text { Evaluate } \int_…

00:44

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00:57

02:45

04:15

Evaluate the integral.

02:10

01:16

here we have to evaluate the interval zero toe a DX and divide way a square plus X squared to the power three divided by two. Now where I'll go into substitute X as eight. Danger Tito So you get d excess. A Sikh in school tutor did Ito. And when x is zero, we get Tita as zero. And when X is a we get Tita ass bye bye full. So the end result will become integration. Zero to bye bye full. And the X is a seeking school teeter lot And do Tito divide by a school as it is plus X square is a square dangerous square Tito, do the power three divide by two it'll be equals 20 to buy by four A seeking school Tito Lord did Ito Onda I'm taking a square common from here so late a square on hair will get one place danger in square Tedo to the power three divide by two and hair also to the power three. Divide by two Let me rate more clearly It will become a square through the power treat. Divide by two on one place Dangerous scripted food of our tree divide by two. Now, after a simplification will get zero to buy by four A Seacon square teeter dot de Tito head It will be a Cuban Lee So a cube times one place opinion square two days seeking schoolteacher Two seconds were treated to about three by two will become sickened Cube Tito Now this seconds creditor on second Cube Readable. Are you really going to cancel? We left with second T only on Dhere We left with one divided by a squared So finally will get and I'm taking one divided by a squared outside zero to buy by four one divide Because Hussein Tita Lord, did he No, It is seeking a second, Tita. Nor did it or not this will week worlds too one divided by a squared zero toe by by four It is a reciprocal off the same thing. So society doesn't delete now again Irrelevant Disentangle easily So integration, of course. 90 days scientist toe one divided by a squared is outside and the limit is from zero to buy. Before I was a bigger problem, It's so one divided by a square hair get signed by by four minus ST zero. So which will be called to one divided by route to a square. So finally we can computer dad integration zero to a DX divided by a squared bless X Square to the power three. Divide by two as equals to one never heard by route to a school. So this is the final answer for the given question.

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