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JEE Main2012MathematicsArea Under CurvesActual

The area of the region bounded by the curve y=x^3 , and the lines, y=8 , and x=0 , is

Options

  1. A8
  2. B12
  3. C10
  4. D16

Correct answer

B. 12

Step-by-step solution

Required Area = _ y=0 ^8 y^ 1 / 3 d y aligned & = . y^ 1 / 3+1 1 3 +1 |₀ ^8= . 3 4 (y^ 4 / 3 ) |₀ ^8 & = 3 4 [(8)^ 4 / 3 -0 ]= 3 4 [2^4 ] & = 3 4 16=12 sq. unit. aligned

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