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Definite Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDefinite Integrals1 Mark
Question
$\int\limits^1_{-1}|1-\text{x}|\text{dx}$ is equal to:
  1. -2
  2. 2
  3. 0
  4. 4
✓

Answer

  1. $2$

Solution:

$\int\limits^1_{-1}|1-\text{x}|\text{dx}$

$=\int\limits^0_{-1}(1-\text{x})\text{dx}+\int\limits^1_0(1-\text{x})\text{dx}$

$=\Big[\text{x}-\frac{\text{x}^2}{2}\Big]^0_{-1}+\Big[\text{x}-\frac{\text{x}^2}{2}\Big]^1_0$

$=0+1+\frac{1}{2}+1-\frac{1}{2}-0$

$=2$

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