Arc length of a Curve

How does the length of the curve x=t^2, y=t^3, [0,2] come out to be 3/4 + (ln2)/2?

Surface area of revolution

How do I find the surface area obtained by revolving the curve y=x-1 from x=1 to x=4 about the line x= -1?

Volume of water poured in to bowl with iron ball.

A bowl is shaped like a hemisphere with radius R centimeters. An iron ball with radius R/2 centimeters is placed in the bowl and water is poured in to a depth of 2R/3 centimeters. How much water was poured in?

A problem dealing with volume of revolution

A bowl is shaped like a hemisphere with radius R centimeters. An iron ball with radius R/2 centimeters is placed in the bowl and water is poured in to a depth of 2R/3 centimeters. How much water was poured in?

Find the arc length of a Cos curve.

Find the arc length of a full cycle of the Cos curve.

Differential Equation with a Natural Log

Find a general solution for this differential equation. Please see the attached file for the fully formatted problem. dy/dx + 2xy = xe^(-x2+2)

Using De Moivre's theorem.

If tan(A) = 1/2, find the value of tan(5A) Hint: Use De Moivre's theorem.

Finding the maximum of a function.

Find the maximum of the following: f(x)=x^3-2x^2+1, -2<=x<=2

Finding the limit of an expression.

Find the limit of following {1-cos(x)}/x^2 as x->infinity

Evaluating integrals

I'm taking a DE calculus class and I'm having problems figuring out the logic in solving some of the problems. The given integral is improper because both the interval of integration is unbounded and the integrand is unbounded near zero. Investigate its convergence by expressing it a sum of two intergrands-one from 0 to 1 an ...continues