find the area the region lying to the right of x= y^2 + 7y + 5 and to the left of x= 3y+2

Answer 1

The linear expression is to the right with the points of interception at y²+7y = 3y+2 or y²+4y-2 = 0 with zeroes at -2 ± sqrt(6)

We want to add up rectangles of height x_R-x_L and with dy in order to find the area (R=right, L=left)

A = Int from ylow to yhigh of ((3y+2)-(y²+7y))dy or (-y²-4y+2)dy

A = -y³/3 -2y²+2y evaluated from ylow to yhigh

I'll leave the numerical stuff to you. Make sure you check my math.

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