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