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Popular >

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

Solution

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

Solution

\frac{86}{3}

+1

Solution steps

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

Expand

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

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

\int_{0}^{2} 16 x^{2} d x = \frac{128}{3}

\int_{0}^{2} 8 x d x = 16

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

= \frac{128}{3} - 16 + 2

Simplify

\frac{128}{3} - 16 + 2 : \frac{86}{3}

= \frac{86}{3}

Popular Examples

integral from 5 to 2 of x^2

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

integral from-1 to 3 of x^2-2x

\int_{- 1}^{3} x^{2} - 2 x d x

integral from-1 to 2 of 6x

\int_{- 1}^{2} 6 x d x

integral from-1 to 1 of 1+x^2

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

integral from 0 to 2 of 2^{5x}

\int_{0}^{2} 2^{5 x} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of (4x-1)^2 ?
The integral from 0 to 2 of (4x-1)^2 is 86/3