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Popular >

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

Solution

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

Solution

\frac{8}{3}

+1

Decimal

2.66666 \dots

Solution steps

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

Expand

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

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

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} 2 x d x = 8

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

= \frac{26}{3} - 8 + 2

Simplify

\frac{26}{3} - 8 + 2 : \frac{8}{3}

= \frac{8}{3}

Graph

Popular Examples

integral from 0 to 2 of 3x(2-x)

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

integral from 0 to 1 of 10x

\int_{0}^{1} 10 x d x

integral from 0 to 3 of r^3

\int_{0}^{3} r^{3} d r

integral from 0 to 1 of x/(sqrt(3x+1))

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

integral from-2 to-1 of 1/z (y+1/2)

\int_{- 2}^{- 1} \frac{1}{z} (y + \frac{1}{2}) d y

Frequently Asked Questions (FAQ)

What is the integral from 1 to 3 of (x-1)^2 ?
The integral from 1 to 3 of (x-1)^2 is 8/3