Question 92 of 198MediumNUMERICAL
The area (in sq. units) of the region enclosed between the parabola y2=2x and the line x+y=4 is \_\_\_
Answer: 18 Solutions · 1
Official solution
Substituting x=4−y: y2=8−2y⇒y2+2y−8=0⇒y=2,−4.
\[\text{Area}=\int_{-4}^2\left[(4-y)-\frac{y^2}2\right]dy=\left[4y-\frac{y^2}2-\frac{y^3}6\right]_{-4}^2=\frac{14}3-\left(-\frac{40}3\right)=18.\] Answer the question to unlock