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JEE Main 201219 MayOnline
Exam
JEE Main
Year
2012
Date
19 May
Mode
Online
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2012 · 19 May · Online · Mathematics · Area Under Curves

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

The area of the region bounded by the curve y=x3y=x^3, and the lines, y=8y=8, and x=0x=0, isThe area of the region bounded by the curve y=x^3 , and the lines, y=8 , and x=0 , isThe 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=08y1/3dy=\int_{y=0}^8 y^{1 / 3} d y The area of the region bounded by the curve y=x^3 , and the lines, y=8 , and x=0 , is
=y1/3+113+1∣08=34(y4/3)∣08=34[(8)4/3−0]=34[24]=34×16=12 sq. unit. \begin{aligned}& =\left.\frac{y^{1 / 3+1}}{\frac{1}{3}+1}\right|_0 ^8=\left.\frac{3}{4}\left(y^{4 / 3}\right)\right|_0 ^8 \\ & =\frac{3}{4}\left[(8)^{4 / 3}-0\right]=\frac{3}{4}\left[2^4\right] \\ & =\frac{3}{4} \times16=12 \text{ sq. unit. } \end{aligned}
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