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BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Mathematics
Chapter
Area Under Curves

BITSAT 2023 · Paper 1 · 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 isThe area enclosed between the curve y= _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


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

Required area A=∫1−e0ydx=∫1−e0log⁡e(x+e)dxA=\int_{1-e}^0 y d x=\int_{1-e}^0 \log _e(x+e) d x
put x+e=t⇒dx=dtx+e=t \Rightarrow d x=d t also when x=1−e,t=x=1-e, t= 1 and when x=0,t=ex=0, t=e
∴A=∫1elog⁡etdt=[tlog⁡et−t]1e\therefore A=\int_1^e \log _e t d t=\left[t \log _e t-t\right]_1^e
e−e−0+1=1e-e-0+1=1
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