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KCET2013MathematicsArea Under Curves

The area bounded by the curve y= ( x 3 ) , x -axis and lines x=0 and x=3 is

Options

  1. A9
  2. B0
  3. C6
  4. D3

Correct answer

C. 6

Step-by-step solution

Required area = _ x=0 ^ x=3 y d x= ₀^ 3 ( x 3 ) d x Let x 3 =t d x=3 d t Also, when x=0t=0x=3 = Then, When t= Then, required area = ₀^ t(3 d t)=3[- t]₀^ =-3[ - 0]=-3(-1-1)=-3(-2)=6

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