Question 1180071

If the area (in square units) of the region under the curve of the function f(x)=5,on the interval from x=4 to x=8 is 20 square units, what is the value of a?


The function {{{y = f(x) = 5 }}}is simply a {{{horizontal}}} straight line.

the interval {{{x=a }}}and {{{x= 8 }}}represent vertical straight lines that intersect {{{x = a}}} and {{{x = 8}}}

the area above the {{{x}}}-axis that is bound by {{{f(x) }}}on the top and {{{x=a}}} & {{{x=8}}} on the sides is simply a {{{rectangle}}} with {{{height = 5}}} and {{{length = ( 8 - a )}}}, and its area is given by

{{{area = height * length = 5 (8-a)}}}

if {{{area =20}}}, then

 {{{5 (8-a)=20}}}

 {{{(8-a)=20/5}}}

 {{{8-a=4}}}

{{{8-4=a}}}

{{{a=4}}}



answer: a. {{{4}}}