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Popular >

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

Solution

\int_{0}^{4} ∣ 1 - 2 x ∣ d x

Solution

\frac{25}{2}

+1

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}

Popular Examples

integral from-1 to 0 of (3t)/((5+t^2)^4)

\int_{- 1}^{0} \frac{3 t}{( 5 + t ^{2} ) ^{4}} d t

integral from 0 to 1/2 of 96x^2y^3

\int_{0}^{\frac{1}{2}} 96 x^{2} y^{3} d x

integral from 1 to 2 of 1/((x-1)(x-3))

\int_{1}^{2} \frac{1}{( x - 1 ) ( x - 3 )} d x

integral from e to 2e of xln(x^3)

\int_{e}^{2 e} x ln (x^{3}) d x

integral from 7 to infinity of 7/(x^3)

\int_{7}^{\infty} \frac{7}{x ^{3}} d x

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