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Steps of double integration

Posted on 2005-04-28
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Integrate the expression & indicate all the steps involved
Integration btn x=-2&+2( Integration y=-2&+2( (dx.dy)/(x^2+y^2+25)^1.5))
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Question by:mhapsekar
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by:aburr
ID: 13895757
A start
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integrate first on x treating y as a constant.
Then integrate on y (the x will ave disappeared.

If you need more help, reply with what you have done and the step at which you were studk
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BigRat earned 375 total points
ID: 13895805
This looks like homework but here are the steps.

1. We first perform the inner integration with respect to y.

2. Note that the integrand is a surd :-

       sqrt( (x²+25+y²)³)

   and put x²+25 equal to a², and put y to atan(t) giving dy = d(atan(t)) =asec²t

   and the surd becomes (asec(t))^4 since 1+tan²=sec².

3. Solve the integral :- (1/a)*cos(t)^4dt;

4. Substitute back t = sqrt(x²+5²)*y.

5. Set y=2 in the equation from 4, and set y=-2, and substract the equations, this is the integrand for the next step.

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