Question

please solve it
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Answer 1

Answer:

Step-by-step explanation:

We have,

$\displaystyle\tt{I=\int^{1}_{-1}|x|\,dx}$

$\bigstar\,\,\blue{\tt{|x|=\begin{cases}\tt{x,\,\,\,\,\,\,\,\,x\ge0}\\\tt{-x,\,\,\,\,x<0}\end{cases}}}$

So,

$\displaystyle\tt{I=-\int^{0}_{-1}x\,dx+\int^{1}_{0}x\,dx}$

$\displaystyle\tt{\implies\,I=-\left[\dfrac{x^2}{2}\right]^{0}_{-1}+\left[\dfrac{x^2}{2}\right]^{1}_{0}}$

$\displaystyle\tt{\implies\,I=-\left[\dfrac{0}{2}-\dfrac{1}{2}\right]+\left[\dfrac{1}{2}-\dfrac{0}{2}\right]}$

$\displaystyle\tt{\implies\,I=\dfrac{1}{2}+\dfrac{1}{2}}$

$\displaystyle\tt{\implies\,I=1}$