Application of DerivativeHard

Question

The slope of tangent to a curve y = f (x) in [x, f (x)] is 2x + 1 If the curve passes through the point (1, 2) then the area bounded by the curve, the x-axis and line x = 1 is

Options

A.5/6
B.6/5
C.1/6
D.6

Solution

       
Given, = 2x + 1
On integrating both sides
        ∫dy = ∫(2x + 1)dx
⇒     y = x2 + x + c which passes through (1,2)
∴     2 = 1 + 1 + c ⇒ c = 0
∴     y = x2 + x
Thus the required area bounded by x axis , the curve and x = 1
        (x2 + x)dx
        sq unit

Create a free account to view solution

View Solution Free
Topic: Application of Derivative·Practice all Application of Derivative questions

More Application of Derivative Questions

For the parabola y2 = 4ax, the ratio of the subtangent to the abscissa is -...The equation of the tangent to the curve 1/√x + 1/√y = 2/√a at point (a, a) is-...If P is a point on the curve 5x2 + 3xy + y2 = 2 and O is the origin, then OP has...The surface area of a spherical bubble is increasing at the rate of 2 cm2/s. When the radius of the bubble is 6 cm, then...The length of the subtangent at any point of the curve y = ax3 is-...