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Popular >

integral from 0 to 1 of (x-1)^2

Solution

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

Solution

\frac{1}{3}

+1

Decimal Notation

0.33333 \dots

Solution steps

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

Expand

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

= \int_{0}^{1} 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_{0}^{1} x^{2} d x - \int_{0}^{1} 2 x d x + \int_{0}^{1} 1 d x

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

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

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

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

Simplify

= \frac{1}{3}

Popular Examples

integral from 0 to 1 of 1/(1+x^4)

\int_{0}^{1} \frac{1}{1 + x ^{4}} d x

integral from 0 to x^2 of 3sin(t)

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

integral from 1 to 5 of 1/(x-3)

\int_{1}^{5} \frac{1}{x - 3} d x

integral from 0 to t of sin(t)

\int_{0}^{t} sin (t) d t

integral from 0 to pi/2 of sin(2x)cos(x)

\int_{0}^{\frac{π}{2}} sin (2 x) cos (x) d x

Frequently Asked Questions (FAQ)

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