Question

Find the area of the region enclosed by the inner loop of the curve r = 48sin(θ)?

Answer 1

To find the area of the region enclosed by the inner loop of the curve r = 48sin(θ), we can use the formula for the area of a polar region, which is A = πr².

Step-by-step explanation:

To find the area of the region enclosed by the inner loop of the curve r = 48sin(θ), we can use the formula for the area of a polar region, which is A = πr². In this case, the radius r is given as 48sin(θ). Substituting this into the area formula, we get A = π(48sin(θ))².

Simplifying further, we have A = π*48²sin(θ)² = 2304πsin(θ)².

Therefore, the area of the region enclosed by the inner loop of the curve r = 48sin(θ) is 2304πsin(θ)².