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

If = 0 and a, b, c are not in A.P., then -...If tangents are drawn from the origin to the curve y = sin x, then their points of contact lie on the curve...The coordinates of the point(s) on the graph of the function, f(x) = + 7x - 4 where the tangent drawn cut off intercepts...The angle of intersection between the curvesy2 = 8x and x2 = 4y - 12 at (2, 4) is-...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...