Question

The double integral for the area inside a circle in polar coordinates is expressed as __________.

A) r² dr dθ
B) 2πr dr dθ
C) ∫∫ r dr dθ
D) πr² dr dθ

Answer 1

The double integral for the area inside a circle in polar coordinates is expressed as D) πr² dr dθ.

Step-by-step explanation:

e double integral for the area inside a circle in polar coordinates is expressed as D) πr² dr dθ. Let's break it down step-by-step:

The area element in polar coordinates is given by dA = r dr dθ.

The limits of integration for r are from 0 to R, where R is the radius of the circle.

Integrating dA over the specified limits of integration gives us the double integral ∫∫ r dr dθ.

The final expression for the double integral is πr² dr dθ.