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

The coordinates of the points on the curve x = a (θ + sin θ), y = a (1−cos θ), where tangent is inc...The point on the curve y = x2 - 3x + 2 at which the tangent is perpendicular to the line y = x is-...The angle of intersection of curves 2y = x3 and y2 = 32 x at the origin is-...Let f(x) = 40/(3x4 + 8x3 - 18x2 + 60). Which of the following statement(s) about f(x) is (are) correct ?...The angle of intersection between the curve y = 4x2 and y = x2 is -...