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Popular >

integral from-2 to 4 of (x-1)^2

Solution

\int_{- 2}^{4} (x - 1)^{2} d x

Solution

18

Solution steps

\int_{- 2}^{4} (x - 1)^{2} d x

Expand

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

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

\int_{- 2}^{4} x^{2} d x = 24

\int_{- 2}^{4} 2 x d x = 12

\int_{- 2}^{4} 1 d x = 6

= 24 - 12 + 6

Simplify

= 18

Graph

Popular Examples

integral from 1 to 4 of (32x+14)

\int_{1}^{4} (32 x + 14) d x

integral from 3 to 4 of x^3-pix^2

\int_{3}^{4} x^{3} - π x^{2} d x

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

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

integral from 0 to 1 of (4x+7)

\int_{0}^{1} (4 x + 7) d x

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

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

Frequently Asked Questions (FAQ)

What is the integral from-2 to 4 of (x-1)^2 ?
The integral from-2 to 4 of (x-1)^2 is 18