矩形区域上的二重积分

Fubini's theorem turns one integral into two

A worked evaluation

Using the integral as a geometric object

When the inner antiderivative is a function

What is $\int_0^1 \int_0^2 (x^2 + y)\, dx\, dy$, integrating in $x$ first?

The integral of $x^2 + y$ over $[0,2] \times [0,1]$ is $11/3$. What is the function's average value there?

For $\iint_{[0,1] \times [0,1]} x e^{x y}\, dA$, which order keeps the work clean?

Compute the inner integral $\int_0^1 (x^2 + y)\, dy$ with $x$ frozen, giving the result in the form a*x^2+b like 3*x^2+1/2.

Give $\iint_R 1\, dA$ over the rectangle $[3, 5] \times [-2, 4]$, as a plain number.