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When we use rectangular coordinates to approximate the area of a region, we subdivide the region into vertical strips and use a sum of areas of rectangles to approximate the area. Explain why we use a “wedge” (i.e., a sector of a circle) and not a rectangle when we use polar coordinates to compute an area.

Short Answer

Expert verified

The region's area is approximated using "wedges," which refers to a circle's sector.

A wedge-shaped slice of the region is determined by a minor change inΔθ

Step by step solution

01

Given information

Consider a function r=f(θ)in polar coordinates. Where θis angular rotation

02

Explain why we use a “wedge” and not a rectangle when we use polar coordinates to compute an area.

A circle's area is calculated by splitting it into an infinite number of wedges produced by radii drawn from the center. When these wedges are rearranged, they form a rectangle with a height equal to the circle's radius and a base length equal to half of the circle's diameter.

The region's area is approximated using "wedges," which refers to a circle's sector.

A wedge-shaped slice of the region is determined by a minor change inΔθ

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