Question

If a < 0 < b , then $\underset{a}{\stackrel{b}{\int }}\frac{|x|}{x}dx=$

• A. $b-a$
• B. $a-b$
• C. $a+b$
• D. $0$

Answer 1

The correct option is C $a+b$

Now,

$\underset{a}{\overset{b}{\int }}\frac{|x|}{x}dx$; [ $a<0<b$]

$=\underset{a}{\overset{0}{\int }}\frac{|x|}{x}dx$$+\underset{0}{\overset{b}{\int }}\frac{|x|}{x}dx$

$=\underset{a}{\overset{0}{\int }}\frac{-x}{x}dx$$+\underset{0}{\overset{b}{\int }}\frac{x}{x}dx$

$=\underset{a}{\overset{0}{\int }}(-1)dx$$+\underset{0}{\overset{b}{\int }}\left(1\right)dx$

$=-(0-a)+(b-0)$

$=b+a$.