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)

Equation for tangent line in cartesian coordinates

Find equation of tangent line in cartesian coordinates. Give in polar coordinates: r=3-2costheta, at theta=pie divided by 3.

Length of curve

length of curve interval [0,4] y= x (to the three halves) minus 1 y=x^3/2 - 1

Arc length of graph of function for a given interval.

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

Volume Calculation of a Cone: Changing radius at Constant Height

Derive a formula that estimates the change that occurs in the volume of a right circular cone when the radius changes from r0 to r1 and the height does not change.

Volume of Revolution: Parabola and Lines

Find the volume of the solid generated by revolving the region between the parabola x = y^2 + 1 and the line x =3 about the line x =3.

Differentiation: Word problem - rate of change

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1m higher than the bow of the boat. If the rope is pulled in at a rate of 1m/s, how fast is the boat approaching the dock when it is 8m from the dock?