The figure shows a `DeltaAOB` and the parabola `y = x^(2)`. The ratio of the area of the `DeltaAOB` to the area of the region AOB of the parabola `y = x^(2)` is equal to

Options

A. `(3)/(5)`
B. `(3)/(4)`
C. `(7)/(8)`
D. `(5)/(6)`

Answer

B

Explanation

Area of curve `OAB=2int_(0)^(a^(2))xdy`

`=2int_(0)^(a^(2))sqrt(y)dy=2[(y^(3//2))/(3//2)]_(0)^(a^(2))=(4)/(3)[a^(3)]`
Now, area of `DeltaOAB=(1)/(2)xxABxxOC`
`=(1)/(2)xx2axxa^(2)=a^(3)`
`therefore ("Area of "DeltaAOB)/("Area of curve AOB")=(a^(3))/((4)/(3)a^(3))=(3)/(4)`