MAT 302 Assignment Problem 7.4

MAT 302 Assignment Problem 7.4 | Borough of Manhattan Community College

7.4 Arc length and Surface of Revolution

Question 1

(1 point) Find the arc length of the graph of the function

y=x36+12xy=x36+12x over the interval [1,2]

Question 2

(1 point) Find the arc length of the graph of the function

y=2x32+3y=2x32+3 over the interval [0,9][0,9].

Question 3

(1 point) Find the arc length of the graph of the function

y=ln(cosx)y=ln(cosx) over the interval [0,π3]

Question 4

(1 point) Find the arc length of the graph of the function

y=ln(ex+1ex−1)y=ln(ex+1ex−1) over the interval [[ ln(2),ln(3)ln(2),ln(3) ]]

Hint: This problem will require factoring exex from numerator and denominator a couple of times.

Question 5

(1 point) Set up and evaluate the definite integral for the area of surface generated by revolving the curve about the x-axis.

y=2x√y=2x on interval [4,9]

Question 6

(1 point) Set up and evaluate the definite integral for the area of surface generated by revolving the curve about the x-axis.

y=9−x2−−−−−√y=9−x2 ,       [−2,2]

Question 7

(1 point) Set up and evaluate the definite integral for the area of surface generated by revolving the curve about the x-axis.

y=x2+3y=x2+3 ,       [1,5]