Question 1179691
We need to find the integral of the function {{{f(x) = 5x + 7 }}}with the limits {{{1}}} and {{{b }}}



{{{int((5 x + 7),dx,1,b) = (5 b^2)/2 + 7 b - 19/2}}}


Solve the quadratic equation and get {{{b }}}


{{{5b^2/2+7b-19/2=88}}}........both sides multiply by {{{2}}}

{{{5b^2+14b-19=176}}}

{{{5b^2+14b-19-176=0}}}

{{{5b^2+14b-195=0}}}...factor

{{{5b^2-25b+39b-195=0}}}

{{{(5b^2-25b)+(39b-195)=0}}}

{{{5b(b-5)+39(b-5)=0}}}

{{{(b - 5) (5b + 39) = 0}}}

=>since given that {{{b > 1}}} ,  use solution {{{b=5}}}


in interval [{{{1}}}, {{{5}}}] the area of the region under the curve will be {{{88}}}


{{{int( (5 x + 7), dx,1,5) = 88}}}

<a href="https://ibb.co/vJVD7fq"><img src="https://i.ibb.co/vJVD7fq/area.gif" alt="area" border="0"></a>