What is the integral from 7 to 9 of x^3-10x^2+21x ?

The integral from 7 to 9 of x^3-10x^2+21x is 268/3

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integral from 7 to 9 of x^3-10x^2+21x

\int_{7}^{9} x^{3} - 10 x^{2} + 21 x d x

\frac{268}{3}

Decimal

89.33333 \dots

Solution steps

\int_{7}^{9} x^{3} - 10 x^{2} + 21 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_{7}^{9} x^{3} d x - \int_{7}^{9} 10 x^{2} d x + \int_{7}^{9} 21 x d x

\int_{7}^{9} x^{3} d x = 1040

\int_{7}^{9} 10 x^{2} d x = \frac{3860}{3}

\int_{7}^{9} 21 x d x = 336

= 1040 - \frac{3860}{3} + 336

Simplify

1040 - \frac{3860}{3} + 336 : \frac{268}{3}

= \frac{268}{3}

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What is the integral from 7 to 9 of x^3-10x^2+21x ?
The integral from 7 to 9 of x^3-10x^2+21x is 268/3