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Find the area of the region that lies inside both curves. r = 9 sin(), r = 9 cos()

Sagot :

The area of the region inside both curves r = 9 sin(θ) and r = 9 cos(θ) is 11.56 square units.

What is integration?

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

The curves are:

r = 9 sin(θ) and

r = 9 cos(θ)

On graphing the above curves:

From the graph:

A = (1/2)∫(9sin(θ))2dθ + (1/2)∫(9cos(θ)2dθ

The region is symmetrical about π/4,:

A = 81∫sin2(θ)dθ from 0 to π/4

After solving:

= 11.56 square unit

Thus, the area of the region inside both curves r = 9 sin(θ) and r = 9 cos(θ) is 11.56 square units.

Learn more about integration here:

brainly.com/question/18125359

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