What is the integral from 1 to 4 of x^2-sqrt(x) ?

The integral from 1 to 4 of x^2-sqrt(x) is 49/3

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integral from 1 to 4 of x^2-sqrt(x)

\int_{1}^{4} x^{2} - x d x

\frac{49}{3}

Decimal

16.33333 \dots

Solution steps

\int_{1}^{4} x^{2} - 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}^{4} x^{2} d x - \int_{1}^{4} x d x

\int_{1}^{4} x^{2} d x = 21

\int_{1}^{4} x d x = \frac{14}{3}

= 21 - \frac{14}{3}

Simplify

21 - \frac{14}{3} : \frac{49}{3}

= \frac{49}{3}

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What is the integral from 1 to 4 of x^2-sqrt(x) ?
The integral from 1 to 4 of x^2-sqrt(x) is 49/3