What is the integral from 0 to 1 of (x^2+3x+1) ?

The integral from 0 to 1 of (x^2+3x+1) is 17/6

Popular >

integral from 0 to 1 of (x^2+3x+1)

\int_{0}^{1} (x^{2} + 3 x + 1) d x

\frac{17}{6}

Decimal

2.83333 \dots

Solution steps

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

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

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

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

= \frac{1}{3} + \frac{3}{2} + 1

Simplify

\frac{1}{3} + \frac{3}{2} + 1 : \frac{17}{6}

= \frac{17}{6}

\int_{- 1}^{1} cos^{3} (x) d x

\int_{1}^{2} x (2 - x)^{99} d x

\int_{- 2}^{2} 9 - \frac{9}{4} x^{2} d x

\int_{2}^{\infty} \frac{1}{x ^{6}} d x

\int_{0}^{2} \frac{r}{4 - r ^{2}} d r

What is the integral from 0 to 1 of (x^2+3x+1) ?
The integral from 0 to 1 of (x^2+3x+1) is 17/6