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Popular >

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

Solution

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

Solution

\frac{1}{3}

+1

Decimal Notation

0.33333 \dots

Solution steps

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

Expand

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

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

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

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

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

= \frac{7}{3} - 3 + 1

Simplify

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

= \frac{1}{3}

Popular Examples

derivative of ln(x+b)

\frac{d}{d x} (ln (x + b))

derivative of x^2+x-1

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

integral of (3-1/(x^4))

\int (3 - \frac{1}{x ^{4}}) d x

derivative of cos(2xdx)

\frac{d}{d x} (cos (2 x) d x)

derivative of (x^2-2^2)

\frac{d}{d x} ((x^{2} - 2)^{2})

Frequently Asked Questions (FAQ)

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