Section 17.1: Double integrals: Riemann sums
Problem types
- Estimation
- Identification
Estimation:
If $R = [0,4] \times [-1,2]$, use a Riemann sum with $m = 2$, $n = 3$ to estimate the value of $\iint_R (1-xy^2) dA$.
Take sample points to be
- the lower right corners and
- the upper left corners of the rectangles.
Identification:
Evaluate the double integral by first identifying it as the volume of a solid.
- $\iint_R (4-2y) dA$, $R = [0,1] \times [0,1]$
- $\iint_R \sqrt{9-y^2} dA$, $R = [0,3] \times [0,3]$.