Can someone help me with this math question about the intersection of circles?

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From the attached image —————> sin(½θ) = ⅗ and cos(½θ) = ⅘

sin(θ) = sin(½θ + ½θ)

sin(θ) = 2sin(½θ)cos(½θ)

sin(θ) = 2(⅗)(⅘)

sin(θ) = 0.96

θ = 1.287 rad

R = 3, r = 5, b = 6, h = 4

Area of shaded region

= ( semicircle area ) - ( area of sector - area of triangle )

= ½πR² - ( ½θr² - ½bh )

= ½π*3² - ( ½*1.287*5² - ½*6*4 )

= 10.05 cm²

You need to take the integral from -3 to 3 of the upper bound line - the lower bound line.

The formula for the lines is easy since you just have simple circles. The answer works out to be about 10.05

Draw the line connecting the two points of intersection (from (-3,4) to (3,4).

Determine the area of the smaller segment of the larger circle.

Subtract that from the area of the semcircle (of the smaller circle).