Q22 of 26 Page 1

Using integration, find the area bounded by the tangent to the curve 4y = x2 at the point (2, 1) and the lines whose equations are x =2y and x = 3y–3.

Given Data:


Parabolic Curve 4y = x2


Equation of lines: x =2y and x = 3y–3


Calculation:


Now differentiating the curve 4y = x2 w.r.t x




At point (2, 1),




Equation of a tangent passing through (2, 1)




y = x – 1


Plot of all the equations are given in figure


The area bound by the three lines can be found as






A = 1 square units


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