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Solve the following.
Evaluate: ∫₀⁶ |x + 3| dx
Evaluate: $\int_0^6 |x + 3| dx$
Answer
Answer
Integral: $\int_{0}^{6} \left(x + 3\right) dx$
For $0 \le x \le 6$, $x + 3 > 0$, so $|x+3| = x + 3$.
$\int_0^6 (x+3)\,dx = \left[\frac{x^2}{2} + 3x\right]_0^6 = 18 + 18 = 36$
Final answer: 36