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

The integral from 0 to 2 of (2x-1)^2 is 14/3

Popular >

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

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

\frac{14}{3}

Decimal Notation

4.66666 \dots

Solution steps

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

Expand

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

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

\int_{0}^{2} 4 x^{2} d x = \frac{32}{3}

\int_{0}^{2} 4 x d x = 8

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

= \frac{32}{3} - 8 + 2

Simplify

\frac{32}{3} - 8 + 2 : \frac{14}{3}

= \frac{14}{3}

\int sec (3 t) tan (3 t) d t

y^{^{''}} + 5 y^{^{'}} + 10 y = 510 e^{2 t} cos (6 t)

\int \frac{x ^{2}}{6 x - x ^{2}} d x

y^{^{'}} + x y = e^{x} y

\int \frac{8 t ^{3} + 10}{4 t ^{2} - 4 t + 5} d t

What is the integral from 0 to 2 of (2x-1)^2 ?
The integral from 0 to 2 of (2x-1)^2 is 14/3