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

Calculating the length of a curve.

Find the length of the curve y=e^-x, 0<_x<_1

Integration

for problem #1, its the integral from o to infinity (the symbol for infinity for that problem was cut off)

Arc length of graph of function for interval.

arc length of the graph of function y=x (to the 2/3)-1 interval[0,4]

Integration

integral x-1, divided by x to the 3rd + x squared to dx. x-1 ----- X to the 3rd + X to the 2nd ( all dx)