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KCET2020MathematicsApplication of Derivatives

The area of the region bounded by the line y=2 x+1, X -axis and the ordinates x=-1 and x=1 is

Options

  1. A9 4
  2. B2
  3. C5 2
  4. D5

Correct answer

C. 5 2

Step-by-step solution

Given, equation of line y=2 x+1...(i) Eq. (i) passing through the points ( -1 2 , 0 ) and (0,1) . Required area of shaded region aligned &= _ -1 ^ -1 / 2 -(2 x+1) d x+ Area of A B C &=- [2 ( x² 2 )+x ]_ -1 ^ -1 / 2 + 1 2 A B B C &=- [x²+x ]_ -1 ^ -1 / 2 + 1 2 3 2 3 &=- [ (- 1 2 )²+ (- 1 2 )-(-1)²-(-1) ]+ 9 4 &=- [ 1 4 - 1 2 ]+ 9 4 &= 1 4 + 9 4 = 10 4 = 5 2 sq units aligned

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