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JEE Main 2005
Exam
JEE Main
Year
2005
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2005 · Mathematics · Area Under Curves

The area enclosed between the curve y= _e(x+e) and the coordinate...

The area enclosed between the curve y=log⁡e(x+e)y=\log _e(x+e) and the coordinate axes is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

A. 1

Step-by-step solution

 Required area (OAB)=∫1−e0ln⁡(x+e)dx=[xln⁡(x+e)−∫1x+exdx]01=1.\begin{aligned}& \text{ Required area }(O A B)=\int_{1-e}^0 \ln (x+e) d x \\ & =\left[x \ln (x+e)-\int \frac{1}{x+e}x d x\right]_0^1=1 . \end{aligned}
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