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Popular >

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

Solution

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

Solution

\frac{7}{3}

+1

Decimal

2.33333 \dots

Solution steps

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

Expand

(x - 3)^{2} : x^{2} - 6 x + 9

= \int_{1}^{2} x^{2} - 6 x + 9 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} 6 x d x + \int_{1}^{2} 9 d x

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

\int_{1}^{2} 6 x d x = 9

\int_{1}^{2} 9 d x = 9

= \frac{7}{3} - 9 + 9

Simplify

= \frac{7}{3}

Graph

Popular Examples

integral from 1 to 2 of ln(1+2^x)

\int_{1}^{2} ln (1 + 2^{x}) d x

integral from 0 to 1 of (2x^e+7e^x)

\int_{0}^{1} (2 x^{e} + 7 e^{x}) d x

integral from 4 to 9 of (sqrt(x)+x)

\int_{4}^{9} (x + x) d x

integral from 1 to 9 of (e^x)/x

\int_{1}^{9} \frac{e ^{x}}{x} d x

integral from a to x of 1/x

\int_{a}^{x} \frac{1}{x} d x

Frequently Asked Questions (FAQ)

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