What is the integral from-2 to 3 of 8x^3+4x^2-7 ?

The integral from-2 to 3 of 8x^3+4x^2-7 is 425/3

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integral from-2 to 3 of 8x^3+4x^2-7

\int_{- 2}^{3} 8 x^{3} + 4 x^{2} - 7 d x

\frac{425}{3}

Decimal

141.66666 \dots

Solution steps

\int_{- 2}^{3} 8 x^{3} + 4 x^{2} - 7 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} 8 x^{3} d x + \int_{- 2}^{3} 4 x^{2} d x - \int_{- 2}^{3} 7 d x

\int_{- 2}^{3} 8 x^{3} d x = 130

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

\int_{- 2}^{3} 7 d x = 35

= 130 + \frac{140}{3} - 35

Simplify

130 + \frac{140}{3} - 35 : \frac{425}{3}

= \frac{425}{3}

\int_{- 9}^{9} ∣ x ∣ d x

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\int_{2}^{3} (x^{2} + x - 12) d x

What is the integral from-2 to 3 of 8x^3+4x^2-7 ?
The integral from-2 to 3 of 8x^3+4x^2-7 is 425/3