about to only mathematics

Options

A. `(3)/(2)`
B. `(4)/(3)`
C. `(5)/(6)`
D. `(1)/(12)`

Answer

C

Explanation

Given, `(dy)/(dx)=2x+1`
On integrating both sides
` int dy=int(2x+1)dx `
` rArr y=x^(2)+x+C ` which passes passes through(1,2)
` therefore 2=1+1+C `
` rArr C=0`
` therefore y=x^(2)+x `

Thus, the required area bounded by X-axis, the curve and x=1
`=int_(0)^(1)(x^(2)+x)dx=[x^(3)/(3)+(x^(2))/(2)]_(0)^(1)`
`=(1)/(3)+(1)/(2)=(5)/(6)` sq unit