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Popular Calculus >

integral from 0 to 4 of |1-2x|

Solution

\int_{0}^{4} ∣ 1 - 2 x ∣ d x

Solution

\frac{25}{2}

+1

Decimal

12.5

Solution steps

\int_{0}^{4} ∣ 1 - 2 x ∣ d x

Eliminate Absolutes

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

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

\int_{\frac{1}{2}}^{4} - 1 + 2 x d x = \frac{49}{4}

= \frac{1}{4} + \frac{49}{4}

Simplify

\frac{1}{4} + \frac{49}{4} : \frac{25}{2}

= \frac{25}{2}

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of |1-2x| ?
The integral from 0 to 4 of |1-2x| is 25/2