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Double Integral with a trig function

  1. Aug 4, 2010 #1
    just wondering if i can still do this, attempted the following:

    ʃʃ cos(x+y)dxdy with upper limits of pi/2 and lower limits of 0 for both integrals

    My answer came out as 0.

    Can anyone confirm this?
  2. jcsd
  3. Aug 4, 2010 #2


    Staff: Mentor

    That's what I get.
  4. Aug 4, 2010 #3
    @Mark44 Thankyou, also what method did you use, I used the identity that

    Is there another way of doing it?
  5. Aug 4, 2010 #4


    Staff: Mentor

    Yes. You can integrate cos(x + y) directly. When you integrate cos(x + y) with respect to x (treating y as a constant), you get sin(x + y). Evaluating this at pi/2 and 0 gives sin(pi/2 + y) - sin(y). The sin(pi/2 + y) term can be rewritten as cos(y) using an identity.

    Finally, integrate cos(y) - sin(y) with respect to y, and evaluate the antiderivative at pi/2 and 0.
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