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$$\int_0^T\int_{-x}^{T-x} f(y) dy dx = \int_{-T}^T (T-|y|)f(y) dy$$

I'm so confused, but I can't reach from one side of equality to the other, please help me.

1 Answers 1

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Hint: Draw the set and use Fubini

EDIT: Here is the picture of the set.

enter image description here

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    i knew it's picture and i don't mention to that because of simplicity of asking question but i don't understand yet – 2017-01-12
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    In the first integral integration is done "vertically": as $x$ varies the height/length of the $y$ variable varies. Through Fubini you want to change the order of integration, i.e let $y$ vary and the integrate horizontally. – 2017-01-12