What is the integral from 0 to 3 of x^3-7x^2+12x ?

The integral from 0 to 3 of x^3-7x^2+12x is 45/4

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integral from 0 to 3 of x^3-7x^2+12x

\int_{0}^{3} x^{3} - 7 x^{2} + 12 x d x

\frac{45}{4}

Decimal

11.25

Solution steps

\int_{0}^{3} x^{3} - 7 x^{2} + 12 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_{0}^{3} x^{3} d x - \int_{0}^{3} 7 x^{2} d x + \int_{0}^{3} 12 x d x

\int_{0}^{3} x^{3} d x = \frac{81}{4}

\int_{0}^{3} 7 x^{2} d x = 63

\int_{0}^{3} 12 x d x = 54

= \frac{81}{4} - 63 + 54

Simplify

\frac{81}{4} - 63 + 54 : \frac{45}{4}

= \frac{45}{4}

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What is the integral from 0 to 3 of x^3-7x^2+12x ?
The integral from 0 to 3 of x^3-7x^2+12x is 45/4