What is the integral from 1 to 7 of (-1/3 x^2+3x) ?

The integral from 1 to 7 of (-1/3 x^2+3x) is 34

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integral from 1 to 7 of (-1/3 x^2+3x)

\int_{1}^{7} (- \frac{1}{3} x^{2} + 3 x) d x

34

Solution steps

\int_{1}^{7} - \frac{1}{3} x^{2} + 3 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_{1}^{7} \frac{1}{3} x^{2} d x + \int_{1}^{7} 3 x d x

\int_{1}^{7} \frac{1}{3} x^{2} d x = 38

\int_{1}^{7} 3 x d x = 72

= - 38 + 72

Simplify

= 34

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What is the integral from 1 to 7 of (-1/3 x^2+3x) ?
The integral from 1 to 7 of (-1/3 x^2+3x) is 34