Question
Evaluate $\int_{1}^{3} \int_{2}^{5}(2 x-3 y) \mathrm{d} x \mathrm{~d} y$
Step 1
The integral of $2x - 3y$ with respect to $x$ is $x^2 - 3xy$. Evaluating this from $2$ to $5$ gives: \[ \int_{2}^{5}(2x - 3y) \, dx = \left[ x^2 - 3xy \right]_{2}^{5} = 5^2 - 3 \cdot 5y - (2^2 - 3 \cdot 2y) = 21 - 9y \] Show more…
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