What is the integral from 0 to 1 of (5+6xsqrt(x)) ?

The integral from 0 to 1 of (5+6xsqrt(x)) is 37/5

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integral from 0 to 1 of (5+6xsqrt(x))

\int_{0}^{1} (5 + 6 x x) d x

\frac{37}{5}

Decimal

7.4

Solution steps

\int_{0}^{1} 5 + 6 x 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}^{1} 5 d x + \int_{0}^{1} 6 x x d x

\int_{0}^{1} 5 d x = 5

\int_{0}^{1} 6 x x d x = \frac{12}{5}

= 5 + \frac{12}{5}

Simplify

5 + \frac{12}{5} : \frac{37}{5}

= \frac{37}{5}

What is the integral from 0 to 1 of (5+6xsqrt(x)) ?
The integral from 0 to 1 of (5+6xsqrt(x)) is 37/5