Just challenge your skills
A curve passing through has its slope at any point equal to . Find the area of the region bounded by the curve and the line .
The answer is 9.
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1 solution
y ′ = 2 / ( y − 2 ) ⇒ y ′ y − 2 y ′ = 2 Integrating on both sides gives: y 2 / 2 − 2 y = 2 x + C
I am going to switch x and y to get simple parabola
y = 1 / 4 x ² − x + 2
Line equation becomes:
y = x / 2 + 2
Integrating both from 0 to 6 gives 21-12=9
Hope it helps.