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1. ### Area of the region bounded between two curves with integration by parts

My mistake was in the bounds, which should have been from 1 to 34. Thank you for your help!
2. ### Area of the region bounded between two curves with integration by parts

Homework Statement Find the area bounded between the two curves y=34ln(x) and y=xln(x) Homework Equations Integration by parts: \intudv= uv-\intvdu The Attempt at a Solution First I found the intersection points of the two equation to set the upper and lower bounds. The lower...
3. ### Cylindrical Shells

nevermind, i've got it! sorry for my faulty answer and thank you for correcting my mistake.
4. ### Cylindrical Shells

why would the limits of integration be from 1 to 3 if you are integrating with respect to the x axis?
5. ### Cylindrical Shells

I think the mistake you are making is in the formula that you are integrating. It seems like you were thinking washers while using the shell equation. The general equation to use for the shell method is 2\pi\int R dx(dx can change depending on which variable you are integrating with respect...
6. ### Isosceles Triangular Prism Related Rates Problem

oh!!! I differentiated much too early... thank you so much for your help!!!
7. ### Isosceles Triangular Prism Related Rates Problem

Right! I used the same equation I put before dv/dt=l(1/2b(dh/dt)+1/2h(db/dt)) and, differentiating b=5h, dv/dt=l(1/2b(dh/dt)+1/2h(5dh/dt)) Also, I really appreciate your help!!!
8. ### Isosceles Triangular Prism Related Rates Problem

Once I replaced the db/dt with the 5dh/dt and solved for the problem I got .4817 ft/min but that was incorrect. The equation I used was... 14=9(1/2*5(dh/dt)+1/2*(7/12)5(dh/dt)
9. ### The rate at which the coffee is cooling

Think Newton's Law of Cooling.
10. ### Isosceles Triangular Prism Related Rates Problem

That seems to be just what my problem is... I can't see the relationship between b and h. I tried setting up a triangle and solving for what b is equal to in terms of h but I am still getting the wrong answer. I used cos(theta)=(1/2b)/h, differentiated, and solved for what db/dt was equal to.
11. ### Isosceles Triangular Prism Related Rates Problem

Homework Statement A trough is 9 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 14 ft3/min, how fast is the water level rising when the water is 7 inches deep? I...
12. ### Differentials word problem

genius...thank you!
13. ### Differentials word problem

Homework Statement Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a hemispherical dome with diameter 54 m. Homework Equations dy=dy/dx *dx Surface area of a hemishpere=2pi*r^2 The Attempt at a Solution dy=4pi*r dx dy=4pi*27...