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Popular >

integral from 2 to 3 of (x-1)^2

Solution

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

Solution

\frac{7}{3}

+1

Decimal

2.33333 \dots

Solution steps

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

Expand

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

= \int_{2}^{3} x^{2} - 2 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_{2}^{3} x^{2} d x - \int_{2}^{3} 2 x d x + \int_{2}^{3} 1 d x

\int_{2}^{3} x^{2} d x = \frac{19}{3}

\int_{2}^{3} 2 x d x = 5

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

= \frac{19}{3} - 5 + 1

Simplify

\frac{19}{3} - 5 + 1 : \frac{7}{3}

= \frac{7}{3}

Graph

Popular Examples

integral from-6 to 3 of-x^2-3x

\int_{- 6}^{3} - x^{2} - 3 x d x

integral from-8 to 8 of e

\int_{- 8}^{8} e d x

integral from 0 to 2 of x^2sin(y)

\int_{0}^{2} x^{2} sin (y) d x

integral from 0 to 9 of e^x

\int_{0}^{9} e^{x} d x

integral from 1 to infinity of ln(1/x)

\int_{1}^{\infty} ln (\frac{1}{x}) d x

Frequently Asked Questions (FAQ)

What is the integral from 2 to 3 of (x-1)^2 ?
The integral from 2 to 3 of (x-1)^2 is 7/3