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

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