Steps of double integration

Posted on 2005-04-28
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 26

    Expert Comment

    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

    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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