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Solve the following.
Evaluate: ∫₀¹ |2x + 1| dx
Evaluate: $\int_0^1 |2x + 1|\,dx$
Answer
Answer
Integral: $\int_{0}^{1} \left(2x+1\right) dx$
On $[0, 1]$, $2x + 1 > 0$, so $|2x+1| = 2x+1$.
$\int_0^1 (2x+1)\,dx = \left[x^2 + x\right]_0^1 = 1 + 1 = 2$
Hence the value is $2$.
Final answer: 2