Let `C` be a curve passing through `M(2,2)` such that the slope of the tangent at anypoint 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`i s__`

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