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Popular >

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

Solution

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

Solution

3

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 = 3

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

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

= 3 - 3 + 3

Simplify

= 3

Popular Examples

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

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

integral from 0 to 1 of x^9e^{-x}

\int_{0}^{1} x^{9} e^{- x} d x

integral from 0 to pi of e^{-x}sin(x)

\int_{0}^{π} e^{- x} sin (x) d x

integral from 0 to 2 of 1/((x-1)(x-3))

\int_{0}^{2} \frac{1}{( x - 1 ) ( x - 3 )} d x

integral from 0 to pi/4 of xtan(x)

\int_{0}^{\frac{π}{4}} x tan (x) d x

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 3