For each of the following, evaluate the given double integral without using iteration. Instead, interpret the integral as, for example, an area or a volume.
(a).
(b).
(c).
Problem 2
Let . Evaluate
(a).
(b).
(c).
(d).
Problem 3
For each of the following, evaluate the given double integral using iteration.
(a). Where is the Rectangle where and
(b). Where is the Triangle with Vertices
(c). Where is the Finite Region in the First Quadrant Bounded by the Curves and
(d). Where is the Finite Region in the First Quadrant Bounded by the Coordinate Axes and the Curve
(e). Where is the Region
Problem 4
For each of the following integrals (i) sketch the region of integration, (ii) write an
equivalent double integral with the order of integration reversed and (iii) evaluate both
double integrals.
(a).
(b).
Problem 5
Combine the sum of the two iterated double integrals
into a single iterated double integral with the order of integration reversed.
Problem 6
Consider the integral
(a). Sketch the Domain of Integration
(b). Evaluate the Integral by Reversing the order of Integration
Problem 17
Consider Combine the Sum of the Iterated Integrals into a Single Iterated Integral with the order of Integration Reversed