What is the integral from-2 to 3 of (4x^2+8)-(3x+2) ?

The integral from-2 to 3 of (4x^2+8)-(3x+2) is 415/6

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integral from-2 to 3 of (4x^2+8)-(3x+2)

\int_{- 2}^{3} (4 x^{2} + 8) - (3 x + 2) d x

\frac{415}{6}

Decimal Notation

69.16666 \dots

Solution steps

\int_{- 2}^{3} 4 x^{2} + 8 - (3 x + 2) d x

Simplify

= \int_{- 2}^{3} 4 x^{2} - 3 x + 6 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 2}^{3} 4 x^{2} d x - \int_{- 2}^{3} 3 x d x + \int_{- 2}^{3} 6 d x

\int_{- 2}^{3} 4 x^{2} d x = \frac{140}{3}

\int_{- 2}^{3} 3 x d x = \frac{15}{2}

\int_{- 2}^{3} 6 d x = 30

= \frac{140}{3} - \frac{15}{2} + 30

Simplify

\frac{140}{3} - \frac{15}{2} + 30 : \frac{415}{6}

= \frac{415}{6}

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What is the integral from-2 to 3 of (4x^2+8)-(3x+2) ?
The integral from-2 to 3 of (4x^2+8)-(3x+2) is 415/6