Question 964045
First find the limits of integration.
{{{sqrt(10x)=0.1x^2}}}
{{{10x=0.01x^4}}}
{{{10x-0.01x^4=0}}}
{{{x(10-0.01x^3)=0}}}
Two solutions:
{{{x=0}}}
and
{{{10-0.01x^3=0}}}
{{{0.01x^3=10}}}
{{{x^3=1000}}}
{{{x=10}}}
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*[illustration eta.JPG].
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So then,
{{{A=int((sqrt(10x)-0.1x^2),dx,x=0,10)}}}
{{{A=sqrt(10)(2/3)x^(3/2)-x^3/30+C}}}
Then evaluating between the limits,
{{{A=(2/3)100-100/3}}}
{{{A=100/3}}}