Steps of double integration

Posted on 2005-04-28
Medium Priority
Last Modified: 2012-06-21
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))
Question by:mhapsekar
LVL 27

Expert Comment

ID: 13895757
A start
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
LVL 27

Accepted Solution

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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