Find the value of ∫₋₁¹ |x| , dx — JEE Mathematics
Find the value of $\int_{-1}^{1} |x| \, dx$.
1 Answer
DDilaniJayawardene31
✓ Accepted
· 1mo ago
▲ 3
The function $f(x) = |x|$ is an even function, so $\int_{-1}^{1} |x| \, dx = 2 \int_{0}^{1} |x| \, dx$.
In the interval $[0, 1]$, $|x| = x$.
$$\int_{-1}^{1} |x| \, dx = 2 \int_{0}^{1} x \, dx = 2 \left[ \frac{x^2}{2} \right]_{0}^{1} = 2 \left(\frac{1}{2} - 0\right) = 1$$
Answer: 1
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Discussion (5)
AB
Underrated solution. The way you set it up makes it almost obvious.
T
Is there a faster shortcut for this in the actual exam? Time is tight.
PI
What changes if the medium/conditions were different?
VC
Can someone explain why we ignore the other root here?
VA
Nicely solved. For the exam, write the final boxed answer clearly to avoid losing marks.