What is the integral from 0 to 4 of (2x-1)^2 ?

The integral from 0 to 4 of (2x-1)^2 is 172/3

Popular >

integral from 0 to 4 of (2x-1)^2

\int_{0}^{4} (2 x - 1)^{2} d x

\frac{172}{3}

Solution steps

\int_{0}^{4} (2 x - 1)^{2} d x

Expand

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

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

\int_{0}^{4} 4 x^{2} d x = \frac{256}{3}

\int_{0}^{4} 4 x d x = 32

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

= \frac{256}{3} - 32 + 4

Simplify

\frac{256}{3} - 32 + 4 : \frac{172}{3}

= \frac{172}{3}

\int_{0}^{4} 2 t 1 + t^{2} d t

\int_{0}^{\frac{π}{2}} e^{- 8 x} cos (x) d x

\int_{3}^{6} x^{2} + 3 d x

\int_{1}^{6} \frac{x}{x + 3} d x

\int_{0}^{2} sec^{3} (x) d x

What is the integral from 0 to 4 of (2x-1)^2 ?
The integral from 0 to 4 of (2x-1)^2 is 172/3