What is the integral from 1 to 4 of 5x^2+sqrt(x) ?

The integral from 1 to 4 of 5x^2+sqrt(x) is 329/3

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integral from 1 to 4 of 5x^2+sqrt(x)

\int_{1}^{4} 5 x^{2} + x d x

\frac{329}{3}

Decimal Notation

109.66666 \dots

Solution steps

\int_{1}^{4} 5 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} 5 x^{2} d x + \int_{1}^{4} x d x

\int_{1}^{4} 5 x^{2} d x = 105

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

= 105 + \frac{14}{3}

Simplify

105 + \frac{14}{3} : \frac{329}{3}

= \frac{329}{3}

\int_{0}^{4} e^{- 2 x} d x

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What is the integral from 1 to 4 of 5x^2+sqrt(x) ?
The integral from 1 to 4 of 5x^2+sqrt(x) is 329/3