1. ## integration with modulus

Find the exact ans:
$\displaystyle \int_{-1}^1$ modulus: e^{2x} - e^{-2(x-1)} dx

the solution given was to be

\int_{-1}^{0.5} e^{2x} - e^{-2(x-1)} dx + \int_{0.5}^1 {e^{2x}-e^{-2(x-1)} dx

I dont understand why there is a need to do this. Why cant we integrate directly? Why is it 0.5?

Sorry i didnt why Latex couldnt work. i tried a lot of times

2. Hint: Where is

3. Originally Posted by helloying
Find the exact ans:
$\displaystyle \int_{-1}^1\mid{e^{2x} - e^{-2(x-1)}\mid} dx$

the solution given was to be

$\displaystyle \int_{-1}^{0.5} e^{2x} - e^{-2(x-1)} dx + \int_{0.5}^1 {e^{2x}-e^{-2(x-1)} dx$

I dont understand why there is a need to do this. Why cant we integrate directly? Why is it 0.5?

Sorry i didnt why Latex couldnt work. i tried a lot of times
because, the resultant value which you get by corresponding $\displaystyle x$ value might be positive or negative. so you seperate integral for positive intigral values and negative intigral values.