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KCET2022MathematicsDefinite Integration

₀^ / 2 ^3 d is equal to

Options

  1. A8 23
  2. B7 23
  3. C8 21
  4. D7 21

Correct answer

C. 8 21

Step-by-step solution

Let I= ₀^ / 2 ^3 d Let =t d =d t When =0 t=0 When aligned & = 2 1=1 & I= ₀^1 t ( (-t^2 ) d t= ₀^1 (t^ 1 / 2 -t^ 5 / 2 ) d t . & = [ array r 3 t^2 3 2 array ]₀^1- [ array r 7 t^2 7 2 array ]₀^1= 2 3 [1-0]- 2 7 [1-0] & = 2 3 - 2 7 = 14-6 21 = 8 21 & aligned

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