<p>Evaluate \(\displaystyle\int_0^1|2x-1|\,dx\) [JEE Main 2015]</p>
Step-by-Step Solution
Key Concept: 2x-1=0 at x=1/2. Split: \int_0^(1/2)(1-2x)dx + \int_(1/2)^1(2x-1)dx = 1/4+1/4 = 1/2.
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<p>$$I=\int_0^{1/2}(1-2x)dx+\int_{1/2}^1(2x-1)dx=\left[x-x^2\right]_0^{1/2}+\left[x^2-x\right]_{1/2}^1$$</p>
<p>$=(\frac{1}{2}-\frac{1}{4})+(1-1-\frac{1}{4}+\frac{1}{2})=\frac{1}{4}+\frac{1}{4}=\boxed{\frac{1}{2}}$</p>
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Correct Answer: A