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Math Help - Double Integral

  1. #1
    Member kezman's Avatar
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    Double Integral

    Calculate
    ∫(xsinx + y sin(x+y)) dxdy
    T

    being T = traingle given by the points (1,0) (0,1) (3,3)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kezman View Post
    Calculate
    ∫(xsinx + y sin(x+y)) dxdy
    T

    being T = traingle given by the points (1,0) (0,1) (3,3)
    How is it that no one responded to this question? For the benefit of other users, here's a response, just over 8 months late, hehe

    begin by graphing the region (see below)

    the line connecting (0,1) and (1,0) is y = 1 - x
    the line connecting (1,0) and (3,3) is y = \frac 32 (x - 1)
    the line connecting (0,1) and (3,3) is y = \frac 23x + 1

    clearly we have to split this region into two parts: i will split it up into two intervals, [0,1] and [1,3].

    Thus, \iint_T (x \sin x + y \sin (x + y))~dxdy = \iint_T (x \sin x + y \sin (x + y))~dydx =  \int_0^1 \int_{1 - x}^{(2/3)x + 1} (x \sin x + y \sin (x + y))~dydx + \int_1^3 \int_{(3/2)(x - 1)}^{(2/3)x + 1} (x \sin x + y \sin (x + y))~dydx

    And continue ... what? ou expected me to give the whole solution away?
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