y2=2x⇒y2=2(4−y)
⇒y2+2y−8=0⇒y=−4,2
The point of intersection of y2=2x and x+y=4 are (8,−4) and (2,2)
Area =∫−42((4−y)−2y2)dy=(4y−2y2−6y3)−42
=(8−2−34)−(−16−8+332)
=354=18 Sq.units.
The area (in sq. units) of the region enclosed between the parabola y2=2x and the line x+y=4 is ______.
Held on 24 Jun 2022 · Verified 6 Jul 2026.
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