Question

Evaluate the integral $I={\int }_4^6|5-x|dx$

• A. - 2
• B. 1
• C. \N
• D. 6

Answer 1

The correct option is B 1

The given function is, i.e., $f\left(x\right)=|5-x|=\{5-x,\times <5\{x-5,x>5$
Due to the existence of a critical point and also due to fact that this point is between the lower and upper limits we can split the integral as below.
$\therefore I={\int }_4^6|5-x|dx$
$={\int }_4^5(5-x)dx+{\int }_5^6(x-5).dx=5x{|}_4^5-\frac{x^2}{2}x{|}_4^5+\frac{x^2}{2}{|}_5^6-5x{|}_5^6=5-\frac{9}{2}+\frac{11}{2}-5=\frac{11}{2}-\frac{9}{2}=\frac{2}{2}=1$
Hence option (b) is correct.