Integral of x - 2|x| from -1 to 2

[Shaybay92]

Homework Statement

Integral[ x - 2|x|]dx from [-1,2]

The Attempt at a Solution

Wouldn't it become x^2/2 - 2x^2/2 so x^2/2 - x^2 and then -x^2/2?

So from [-1,2] it would just be

-((2^2)/2) - - ((-1)^2/2) which is -1.5 but the answer is -3.5...

 

[Shaybay92]

dddd

 

[Shaybay92]

Wait, sorry this shouldn't be the issue because from my graph the whole function is negative anyway... any suggestions?

 

[Borek]

I can be wrong, but I would try

$$\int_{-1}^2f(x)dx = \int_{-1}^0f(x)dx + \int_{0}^2f(x)dx$$

 

[Mark44]

I agree with Borek. The idea is that you can eliminate the absolute values by looking at the integrand on [-1, 0] and on [0, 2].

If x <= 0, |x| = -x.
If x >= 0, |x| = x.