Question

If $a<b<0$ then find the value of $\underset{a}{\overset{b}{\int }}\frac{x}{|x|}dx$.

Answer 1

Since $a<b<0$ then $|x|=-x$ in $[a,b]$.

Now,

$\underset{a}{\overset{b}{\int }}\frac{x}{|x|}dx$

$=-\underset{a}{\overset{b}{\int }}\frac{x}{x}dx$

$=-\underset{a}{\overset{b}{\int }}dx$

$=(a-b)$