Compute the area of the region which lies to the right of the parabola x=y^2-12 and to the left of the line y=x.
- رياضيات
- 2021-05-04
- HebaAallahFathy
Compute the area of the region which lies to the right of the parabola x=y^2-12 and to the left of the line y=x.
الأجوبة
Solving the equations to get:
y^2-y-12=0,then y=-3 & y=4
The required area is:
A=∫_(-3)^4[y-(y^2-12)] dy
=[1/2 y^2-1/3 y^3+12y]_(-3)^4
=[8-64/3+48]-[9/2+9-36]=343/6 square units.
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