Evaluate ∫(𝑥+3)√4−𝑥^2𝑑𝑥 by writing it as a sum of two integrals and interpreting one of those integrals in terms of an area.

Answer 1

∫(𝑥+3)√(4−𝑥^2) 𝑑𝑥 = ∫x √(4−𝑥^2) 𝑑𝑥 + 3∫√(4−𝑥^2) 𝑑𝑥
The first term is -1/2 the area under the parabola y=√(4-x^2)^3

The second is 3 times the area under a semicircle of radius 2.

Answer 2

sorry the integral is from x=-2 to x=2 so would the first integral equal to 0?

Answer 3

a=-2, b=2*

Answer 4

no. you just have the full area under the curves.
Go ahead and do the integration!