MAT 1236 Calculus III Section 15.4 Double Integrals In Polar Coordinates

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HW & … WebAssign 15.4 (10 problems, 82 min.)

Preview Formula for double integral if the region is described in polar coordinates consider the case where the bounds are all constants (Polar rectangle) Rectangular and polar regions are in the most popular applications in physics and engineering

Polar Rectangle

Example A

Example B

Example C

Polar Rectangle R

R

Idea

R

Polar Rectangle

Formula Order of integration is not important (why?)

Splitting Formula

Example 1

Remarks Sometimes, an integral in polar coordinates may be easier to evaluate than the corresponding one in rectangular coordinates

Example 2 Evaluate by converting to polar coordinates

Example 2

Addition Formula for 15.4