1. ## Evaluate the Integral

Question : Evaluate the Integral

$\displaystyle \int_{0}^{4} |x-2| dx$

Solution
My work::::::::::::::::::::::::::;;;;;;

$\displaystyle \int_{0}^{4} |x-2| dx$ = $\displaystyle \int_{0}^{4} (x-2) dx$ = $\displaystyle \int_{0}^{4} x dx - \int_{0}^{4} 2 dx$ =.....= $\displaystyle 0$....................Is this correct???

2. No, it's wrong, you can't remove the absolute value bars whenever you like.

$\displaystyle |x-2|=x-2$ when? And $\displaystyle |x-2|=2-x$ when?

3. Originally Posted by zorro
Question : Evaluate the Integral

$\displaystyle \int_{0}^{4} |x-2| dx$

Solution
My work::::::::::::::::::::::::::;;;;;;

$\displaystyle \int_{0}^{4} |x-2| dx$ = $\displaystyle \int_{0}^{4} (x-2) dx$ = $\displaystyle \int_{0}^{4} x dx - \int_{0}^{4} 2 dx$ =.....= $\displaystyle 0$....................Is this correct???
No, it's incorrect.

$\displaystyle |x - 2| = x - 2$ for $\displaystyle x \geq 2$, and $\displaystyle |x - 2| = -(x - 2) = 2 - x$ for $\displaystyle x < 2$.

So $\displaystyle \int_0^4{|x - 2|\,dx} = \int_0^2{2 - x\,dx} + \int_2^4{x - 2\,dx}$.

4. thanks mite i have got the answer as 6.....

5. Originally Posted by zorro
thanks mite i have got the answer as 6.....