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Popular >

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

Solution

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

Solution

\frac{14}{3}

+1

Solution steps

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

Expand

(2 x - 1)^{2} : 4 x^{2} - 4 x + 1

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

\int_{- 1}^{1} 4 x^{2} d x = \frac{8}{3}

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

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

= \frac{8}{3} - 0 + 2

Simplify

\frac{8}{3} - 0 + 2 : \frac{14}{3}

= \frac{14}{3}

Popular Examples

integral of sin^2(14x)

\int sin^{2} (14 x) d x

(dy)/(dx)=-5-5x+y

\frac{d y}{d x} = - 5 - 5 x + y

2 y d x + x^{2} d y = - d x

integral of x^23^{5x^3+1}

\int x^{2} 3^{5 x^{3} + 1} d x

integral from 0 to 1/2 of x^2

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

Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of (2x-1)^2 ?
The integral from-1 to 1 of (2x-1)^2 is 14/3