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Popular >

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

Solution

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

Solution

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

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

Frequently Asked Questions (FAQ)

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