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MHT CET202311 May 2023Evening ShiftMathematicsApplication of DerivativesActual

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

Options

  1. A3 2
  2. B4 3
  3. C5 6
  4. D1 12

Correct answer

C. 5 6

Step-by-step solution

According to the given condition, d y ~d x =2 x+1 Integrating w.r.t. x , we get y=x^2+x+ c As curve passes through (1,2) , we get 2=(1)^2+1+c c=0 The equation of the curve is y=x^2+x . Required area aligned & = ₀^1 (x^2+x ) d x & = [ x^3 3 + x^2 2 ]₀^1 & = 1 3 + 1 2 & = 5 6 sq. units aligned

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