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

The integral from 0 to 1 of x^2(x+1/2) is 5/12

Popular >

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

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

\frac{5}{12}

Decimal Notation

0.41666 \dots

Solution steps

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

Expand

x^{2} (x + \frac{1}{2}) : x^{3} + \frac{x ^{2}}{2}

= \int_{0}^{1} x^{3} + \frac{x ^{2}}{2} 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} x^{3} d x + \int_{0}^{1} \frac{x ^{2}}{2} d x

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

\int_{0}^{1} \frac{x ^{2}}{2} d x = \frac{1}{6}

= \frac{1}{4} + \frac{1}{6}

Simplify

\frac{1}{4} + \frac{1}{6} : \frac{5}{12}

= \frac{5}{12}

\int_{0}^{1} 10 e^{x + 3} d x

\int_{0}^{4} (x^{2} - 2 x) d x

\int_{0}^{3} e^{3 x} d x

\int_{1}^{4} x 3 - x d x

\int_{x}^{0} t^{2} + 4 d t

What is the integral from 0 to 1 of x^2(x+1/2) ?
The integral from 0 to 1 of x^2(x+1/2) is 5/12