What is the integral from-1 to 3 of (|2-x|+x^2) ?

The integral from-1 to 3 of (|2-x|+x^2) is 43/3

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integral from-1 to 3 of (|2-x|+x^2)

\int_{- 1}^{3} (∣ 2 - x ∣ + x^{2}) d x

\frac{43}{3}

Decimal

14.33333 \dots

Solution steps

\int_{- 1}^{3} ∣ 2 - x ∣ + x^{2} d x

Eliminate Absolutes

= \int_{- 1}^{2} 2 - x + x^{2} d x + \int_{2}^{3} - 2 + x + x^{2} d x

\int_{- 1}^{2} 2 - x + x^{2} d x = \frac{15}{2}

\int_{2}^{3} - 2 + x + x^{2} d x = \frac{41}{6}

= \frac{15}{2} + \frac{41}{6}

Simplify

\frac{15}{2} + \frac{41}{6} : \frac{43}{3}

= \frac{43}{3}

What is the integral from-1 to 3 of (|2-x|+x^2) ?
The integral from-1 to 3 of (|2-x|+x^2) is 43/3