What is the integral from-2 to 3 of (3x^2-5x) ?

The integral from-2 to 3 of (3x^2-5x) is 45/2

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integral from-2 to 3 of (3x^2-5x)

\int_{- 2}^{3} (3 x^{2} - 5 x) d x

\frac{45}{2}

Decimal

22.5

Solution steps

\int_{- 2}^{3} 3 x^{2} - 5 x 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} 3 x^{2} d x - \int_{- 2}^{3} 5 x d x

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

\int_{- 2}^{3} 5 x d x = \frac{25}{2}

= 35 - \frac{25}{2}

Simplify

35 - \frac{25}{2} : \frac{45}{2}

= \frac{45}{2}

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What is the integral from-2 to 3 of (3x^2-5x) ?
The integral from-2 to 3 of (3x^2-5x) is 45/2