SOLUTION: I need help with this please: Find the area of the region in the first quadrant bounded by the graph of y = x {{{sqrt(4

SOLUTION: I need help with this please: Find the area of the region in the first quadrant bounded by the graph of y = x {{{sqrt(4 - x^2)}}}

Question 1022073: I need help with this please: Find the area of the region in the first quadrant bounded by the graph of y = x

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is the integral between 0 and 2 of x*sqrt(4-x^2)
let u=4-x^2
du=-2xdx
(-1/2) du=xdx
integral of -(1/2)u^(1/2)
(-1/2)(2/3)u^(3/2)
(-1/3)*(4-x^2)^(3/2) evaluated at 0 and 2.
at 2, (-1/3)(4-x^2)^(3/2)=0.
at 0, -(-1/3)(4-x^2)^(3/2)=8, because 4^(3/2)=-(-8/3)=8/3
Area is 8/3

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