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}

csc (y) + sec^{2} (x) (\frac{d y}{d x}) = 0

n = 1 \sum \infty \frac{3}{n ( n + 1 )}

f (x) = x, g (x) = x, x = 0, 2

x y^{^{'}} = 8 y - 9 x, y (1) = 0, y (1) = 0

\int \frac{x}{e ^{6 x}} d x

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