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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
The integral $\int \limits_{0}^{2} \| x-1|-x| d x$ is equal to
  • ✓
    $1.5$
  • B
    $2.5$
  • C
    $0.5$
  • D
    $3.5$
✓

Answer

Correct option: A.
$1.5$
a
$\int_{0}^{2}|x-1|-x \mid \mathrm{d} x$

Let $f(x) \| x-1|-x|$

$=\left\{\begin{array}{ll}1, & x \geq 1 \\ |1-2 x|, & x \leq 1\end{array}\right.$

$A=\frac{1}{2}+1=\frac{3}{2}$

Or

$\int_{0}^{1 / 2}(1-2 x) d x+\int_{1 / 2}^{1}(2 x-1)+\int_{0}^{2} 1 d x$

$=\left[x-x^{2}\right]_{0}^{\frac{1}{2}}+\left[x^{2}-x\right]_{1 / 2}^{1}+[x]_{1}^{2}$

$=3 / 2$

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