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Popular >

integral from 0 to 8 of (5-|x-3|)

Solution

\int_{0}^{8} (5 - ∣ x - 3 ∣) d x

Solution

23

Solution steps

\int_{0}^{8} 5 - ∣ x - 3 ∣ d x

Eliminate Absolutes

= \int_{0}^{3} 5 - (- x + 3) d x + \int_{3}^{8} 5 - (x - 3) d x

\int_{0}^{3} 5 - (- x + 3) d x = \frac{21}{2}

\int_{3}^{8} 5 - (x - 3) d x = \frac{25}{2}

= \frac{21}{2} + \frac{25}{2}

Simplify

\frac{21}{2} + \frac{25}{2} : 23

= 23

Graph

Popular Examples

integral of 4x*e^{2x^2}

\int 4 x \cdot e^{2 x^{2}} d x

area f(x)=x^3-6x^2+8x,g(x)=x^2-4x area

f (x) = x^{3} - 6 x^{2} + 8 x, g (x) = x^{2} - 4 x

tangent of 1/((x-7))tangent of

\frac{1}{( x - 7 )}

y^'-y=e^tcos(t),y(0)=1

y^{^{'}} - y = e^{t} cos (t), y (0) = 1

derivative of 5/x-2/(x^3+1/(x^4))

\frac{d}{d x} (\frac{5}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

Frequently Asked Questions (FAQ)

What is the integral from 0 to 8 of (5-|x-3|) ?
The integral from 0 to 8 of (5-|x-3|) is 23