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Popular >

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

Solution

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

Solution

\frac{7}{3}

+1

Decimal Notation

2.33333 \dots

Solution steps

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

Expand

(x - 2)^{2} : x^{2} - 4 x + 4

= \int_{0}^{1} x^{2} - 4 x + 4 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} 4 x d x + \int_{0}^{1} 4 d x

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

\int_{0}^{1} 4 x d x = 2

\int_{0}^{1} 4 d x = 4

= \frac{1}{3} - 2 + 4

Simplify

\frac{1}{3} - 2 + 4 : \frac{7}{3}

= \frac{7}{3}

Popular Examples

integral from 0 to 1 of x*4(x-x^3)

\int_{0}^{1} x \cdot 4 (x - x^{3}) d x

integral from 0 to pi of cos(nt)

\int_{0}^{π} cos (n t) d t

integral from 1 to 5 of (1/x)

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

integral from 1 to infinity of 1/(3^x)

\int_{1}^{\infty} \frac{1}{3 ^{x}} d x

integral from 1 to infinity of 3x^{-3}

\int_{1}^{\infty} 3 x^{- 3} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of (x-2)^2 ?
The integral from 0 to 1 of (x-2)^2 is 7/3