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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Area Under Curves

NTA Abhyas 2020 · Mathematics · Area Under Curves

The area bounded by y = xe^ |x| and the lines |x| = 1, y = 0 is

The area bounded by y=xe∣x∣andthelines∣x∣=1,y=0y = xe^{\left|x\right|} and the lines \left|x\right| = 1, y = 0 is

Options

  1. A4squnits4squnits
  2. B6squnits6squnits
  3. C1squnit1squnit
  4. D2squnits2squnits

Correct answer

D. 2squnits2squnits

Step-by-step solution

Since, ∣x∣=1\left|x\right| = 1

∴x=±1∴ x = \pm 1

∴ y = xe^{\left|x\right|} = \left\{xe−x,−1<x<0xex,0<x<1\begin{array}{ll}xe^{- x} , - 1 < x < 0 \\ xe^{x} , 0 < x < 1\end{array}\right\}

∴∴ Required area =∣∫−10xe−xdx∣+∣∫01xexdx∣= \left|{∫}_{- 1}^{0}xe^{- x}dx\right| + \left|{∫}_{0}^{1}xe^{x}dx\right|

\left|{- xe^{- x} - e^{- x}}_{- 1}^{0}\right| + \left|{xe^{x} - e^{x}}_{0}^{1}\right|<br/><br/><br /><br />= 1 + 1 = 2squnits
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