Let C be a curve passing through M(2,2) such that the slope of the tangent at any point to the curve is reciprocal of the ordinate of the point. If the area bounded by curve C and line x=2 is A, then the value of `(3A)/(2)` is__.

Answer

8

Explanation

Let P(x,y) be any point on the curve C.
`"Now, "(dy)/(dx)=(1)/(y)`
`"or "ydy=dxrArr(y^(2))/(2)=x+k`
Since the curve passes through M(2,2), so k=0
`rArr" "y^(2)=2x`
`therefore" Required area "=2overset(2)underset(0)intsqrt(2x)dx=2sqrt(2)xx(2)/(3)(x^(3//2))_(0)^(2)`
`=(4)/(3)sqrt(2)xx2sqrt(2)=(16)/(3)` sq. unit