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JEE Main 2011
Exam
JEE Main
Year
2011
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2011 · Mathematics · Area Under Curves

The area of the region enclosed by the curves y=x, x=e, y=(1)/(x)...

The area of the region enclosed by the curves y=x,x=e,y=1xy=x, x=e, y=\frac{1}{x} and the positive xx-axis isThe area of the region enclosed by the curves y=x, x=e, y=(1)/(x) and the positive x -axis is

Options

  1. A1 square units
  2. B32\frac{3}{2} square units
  3. C52\frac{5}{2} square units
  4. D12\frac{1}{2} square units

Correct answer

B. 32\frac{3}{2} square units

Step-by-step solution

The area of the region enclosed by the curves y=x, x=e, y=(1)/(x) and the positive x -axis is
Area =∫01xdx+∫1e1xdx=12+1=32=\int_0^1 x d x+\int_1^e \frac{1}{x} d x=\frac{1}{2}+1=\frac{3}{2}
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