What is the integral from 0 to 6 of (4x-1)^2 ?

The integral from 0 to 6 of (4x-1)^2 is 1014

Popular >

integral from 0 to 6 of (4x-1)^2

\int_{0}^{6} (4 x - 1)^{2} d x

1014

Solution steps

\int_{0}^{6} (4 x - 1)^{2} d x

Expand

(4 x - 1)^{2} : 16 x^{2} - 8 x + 1

= \int_{0}^{6} 16 x^{2} - 8 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}^{6} 16 x^{2} d x - \int_{0}^{6} 8 x d x + \int_{0}^{6} 1 d x

\int_{0}^{6} 16 x^{2} d x = 1152

\int_{0}^{6} 8 x d x = 144

\int_{0}^{6} 1 d x = 6

= 1152 - 144 + 6

Simplify

= 1014

\int_{3}^{9} ∣ sin (x) ∣ d x

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

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

\int_{- 1}^{1} (∣ x ∣ + x) e^{- ∣ x ∣} d x

\int_{2}^{5} 3 x^{2} d x

What is the integral from 0 to 6 of (4x-1)^2 ?
The integral from 0 to 6 of (4x-1)^2 is 1014