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Popular >

integral from 0 to 6 of (3-|x-3|)

Solution

\int_{0}^{6} (3 - ∣ x - 3 ∣) d x

Solution

9

Solution steps

\int_{0}^{6} 3 - ∣ x - 3 ∣ d x

Eliminate Absolutes

= \int_{0}^{3} 3 - (- x + 3) d x + \int_{3}^{6} 3 - (x - 3) d x

\int_{0}^{3} 3 - (- x + 3) d x = \frac{9}{2}

\int_{3}^{6} 3 - (x - 3) d x = \frac{9}{2}

= \frac{9}{2} + \frac{9}{2}

Simplify

\frac{9}{2} + \frac{9}{2} : 9

= 9

Popular Examples

derivative of e^x(4x^2-8x+8)

\frac{d}{d x} (e^{x} (4 x^{2} - 8 x + 8))

derivative of-4e^{-x}

\frac{d}{d x} (- 4 e^{- x})

integral from 1 to 2 of (10ln(x))/(x^2)

\int_{1}^{2} \frac{10 ln ( x )}{x ^{2}} d x

f(x)=arctan(5x)

f (x) = arctan (5 x)

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

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of (3-|x-3|) ?
The integral from 0 to 6 of (3-|x-3|) is 9