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Popular >

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

Solution

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

Solution

\frac{23}{6}

+1

Decimal

3.83333 \dots

Solution steps

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

Expand

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

= \int_{1}^{2} x^{2} + 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_{1}^{2} x^{2} d x + \int_{1}^{2} x d x

\int_{1}^{2} x^{2} d x = \frac{7}{3}

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

= \frac{7}{3} + \frac{3}{2}

Simplify

\frac{7}{3} + \frac{3}{2} : \frac{23}{6}

= \frac{23}{6}

Graph

Popular Examples

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\int_{- 7}^{7} (4 + x + x^{2} + x^{3}) d x

integral from 0 to 2 of 1/(sqrt(x-1))

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

integral from 1 to 3 of ((x^2+5)/x)

\int_{1}^{3} (\frac{x ^{2} + 5}{x}) d x

integral from-5 to 5 of |x+3|

\int_{- 5}^{5} ∣ x + 3 ∣ d x

integral from-10 to 8 of sqrt(80-2x-x^2)

\int_{- 10}^{8} 80 - 2 x - x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to 2 of x(x+1) ?
The integral from 1 to 2 of x(x+1) is 23/6