Question 972421
Find the points of intersection to define the limits of integration.
Not sure if you need to calculate the entire area so I'll break it up integrating from x=-5 to x=0 and then from x=0 to x=4.
.
.
.
*[illustration d3d.JPG].
.
.
.
{{{int((x^3+x^2-20x),dx)=x^4/4+x^3/3-10x^2+C}}}
So then from {{{x=-5}}} to {{{x=0}}}, the area {{{A[1]}}} would be,
{{{A[1]=(0^4-(-5)^4)/4+(0^3-(-5)^3)/3-10(0^2-5^2)}}}
{{{A[1]=(-625)/4+(125)/3+10(25)}}}
{{{A[1]=(-1875)/12+(500)/12+3000/12}}}
{{{A[1]=1625/12}}}
.
.
.
And the area {{{A[2]}}} from {{{x=0}}} to {{{x=4}}} would be,
{{{A[2]=(4^4-(0)^4)/4+(4^3-(0)^3)/3-10(4^2-0^2)}}}
{{{A[2]=64+64/3-160}}}
{{{A[2]=192/3+64/3-480/3}}}
{{{A[2]=-224/3}}}
.
.
.
So the entire area would be,
{{{A=A[1]+A[2]}}}
{{{A=1625/12-224/3}}}
{{{A=1625/12-896/12}}}
{{{A=729/12}}}
{{{highlight(A=243/4)}}}