Question

How do you find the anti derivative of (1-|x|)?

Answer 1

if x>0, then |x|=x

if x<0, then |x|=-x

hope that helps

Answer 2

Maybe I am not asking the question right. its the intrgural from -1 to 1\[\int\limits_{-1}^{1}(1-|X|)dx\]

Answer 3

Sorry does that make more sense?

Answer 4

\[\int\limits_{-1}^{1}|x|dx=\int\limits_{-1}^{0}(-x) dx+\int\limits_{0}^{1}(x) dx\]

Answer 5

\[\frac{-x^2}{2}|_{-1}^{0}+\frac{x^2}{2}|_0^1=[0-\frac{-1}{2}]+[\frac{1}{2}-0]=1\]

Answer 6

so
\[\int\limits_{-1}^{1}(1-|x|)dx=\int\limits_{-1}^{1}1 dx-\int\limits_{-1}^{1}|x| dx\]
\[=x|^1_{-1}-1=[1-(-1)]-1=1+1-1=2-1=1\]