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KCET2010MathematicsArea Under Curves

The area bounded by the curve y= array cl x², & x < 0 x, & x 0 array . and the line y=4 , is

Options

  1. A32 3
  2. B8 3
  3. C40 3
  4. D16 3

Correct answer

C. 40 3

Step-by-step solution

Given, curve y= array c x², x aligned A ₁ &= _ y =0 ⁴ y dy &= [ 2 3 y ^ 3 / 2 ]₀⁴ t &= 2 3 [(4)^ 3 / 2 -0 ] &= 2 3 (2)³ &= 16 3 aligned and area of OBCO , aligned A₂ &= ₀⁴ y d y= [ y² 2 ]₀⁴ &= 1 2 [(4)²-0 ]= 16 2 =8 aligned Hence, area of OABO = A ₁+ A ₂= 16 3 +8= 40 3 sq unit

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