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Math Help - Double integral

  1. #1
    Senior Member Dinkydoe's Avatar
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    Double integral

    I've been given the function:

    f:\mathbb{R}\to\mathbb{R} given by f(x)=\frac{\sin(x)}{x}, x\neq 0 and f(x)=0 otherwise.

    Calculate the double integral:

    \int_0^1 \left(\int_y^1f(x)dx\right)dy

    I'm not sure how to tackle this one, any hints?
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  2. #2
    Member Black's Avatar
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    \int_0^1 \left(\int_y^1 \frac{\sin x}{x} dx \right) dy= \int_0^1 \left(\int_0^x \frac{\sin x}{x} dy\right) dx.
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  3. #3
    Senior Member Dinkydoe's Avatar
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    Thanks I was hoping for something like that,

    However, I have yet to understand why it's legitimate to take that step
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  4. #4
    Member Black's Avatar
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    It follows by investigating the region of integration.
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