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

The integral from 0 to 1 of x(x+1/2) is 7/12

Popular >

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

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

\frac{7}{12}

Decimal

0.58333 \dots

Solution steps

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

Expand

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

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

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

\int_{0}^{1} \frac{x}{2} d x = \frac{1}{4}

= \frac{1}{3} + \frac{1}{4}

Simplify

\frac{1}{3} + \frac{1}{4} : \frac{7}{12}

= \frac{7}{12}

\int_{0}^{\frac{π}{4}} 6 x + sec^{2} (x) - 2 d x

\int_{0}^{1} \frac{1}{1 - t ^{2}} d t

\int_{0}^{π} sin (t) cos (t) d t

\int_{0}^{x^{2}} cos (t^{2}) d t

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

What is the integral from 0 to 1 of x(x+1/2) ?
The integral from 0 to 1 of x(x+1/2) is 7/12