What is the integral from 0 to 4 of (sqrt(x)+3x) ?

The integral from 0 to 4 of (sqrt(x)+3x) is 88/3

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integral from 0 to 4 of (sqrt(x)+3x)

\int_{0}^{4} (x + 3 x) d x

\frac{88}{3}

Decimal

29.33333 \dots

Solution steps

\int_{0}^{4} x + 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_{0}^{4} x d x + \int_{0}^{4} 3 x d x

\int_{0}^{4} x d x = \frac{16}{3}

\int_{0}^{4} 3 x d x = 24

= \frac{16}{3} + 24

Simplify

\frac{16}{3} + 24 : \frac{88}{3}

= \frac{88}{3}

\int e^{x} e^{x} + 5 d x

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

f (x) = \frac{1}{2 x}, at x = 9

f (x) = (x^{4} - \frac{5}{x ^{3}})^{- 4}

\int_{0}^{3} \frac{x}{x + 1} d x

What is the integral from 0 to 4 of (sqrt(x)+3x) ?
The integral from 0 to 4 of (sqrt(x)+3x) is 88/3