What is the integral from 0 to 1 of 10x(5x^2+1) ?

The integral from 0 to 1 of 10x(5x^2+1) is 35/2

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integral from 0 to 1 of 10x(5x^2+1)

\int_{0}^{1} 10 x (5 x^{2} + 1) d x

\frac{35}{2}

Decimal

17.5

Solution steps

\int_{0}^{1} 10 x (5 x^{2} + 1) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int_{0}^{1} x (5 x^{2} + 1) d x

Expand

x (5 x^{2} + 1) : 5 x^{3} + x

= 10 \cdot \int_{0}^{1} 5 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

= 10 (\int_{0}^{1} 5 x^{3} d x + \int_{0}^{1} x d x)

\int_{0}^{1} 5 x^{3} d x = \frac{5}{4}

\int_{0}^{1} x d x = \frac{1}{2}

= 10 (\frac{5}{4} + \frac{1}{2})

Simplify

10 (\frac{5}{4} + \frac{1}{2}) : \frac{35}{2}

= \frac{35}{2}

What is the integral from 0 to 1 of 10x(5x^2+1) ?
The integral from 0 to 1 of 10x(5x^2+1) is 35/2