Question:
The integral $\int^{2} \| x-1|-x| d x$ is equal to_________.
Solution:
$\int_{0}^{2}|x-1|-x \mid d x$
Let $f(x) \| x-1|-x|$
$= \begin{cases}1, & x \geq 1 \\ |1-2 x|, & x \leq 1\end{cases}$
$A=\frac{1}{2}+1=\frac{3}{2}$
or
$\int_{0}^{1 / 2}(1-2 x) d x+\int_{1 / 2}^{1}(2 x-1)+\int_{0}^{2} 1 d x$
$=\left[x-x^{2}\right]_{0}^{1}+\left[x^{2}-x\right]_{1 / 2}^{1}+[x]_{1}^{2}$
$=3 / 2$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.