1). Find Area of the region enclosed by the y-axis and the curves y=x^2 and y=(x^2+x+1)e^-x
2). Coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 10in^3/min.
Then there's a picture of a 6 in. diameter cone, and it also has a height of 6 in. Then the pointy end of the cone is facing down touching a cylinder with a 6 in. diameter. (no height)
How fast is the level in the pot rising when the coffee in the cone is 5 in. deep?
How fast is the level in the cone falling at that moment?
So for the first one, the only I idea i have it to find the point when the 2 equations intersects, would be nice if I can do that without a calculator if possible, then I integrate both equations. Then plug in x for what value it was for when it the equations intersected. Subtract the values of the integral of y=(x^2+x+1)e^-x and y=2x to get my answer, I hope. Please clarify to me if this works.
The second one I'm more clueless in (haven't done this in a while). Ok, so I'm trying to find dh/dt, and I know my dV/dt is -10in.^3/min. Afterward I'm lost in what to do after that. Please explain work and show me how this is done, thank you.