Which of the following?

Question

Which of the following expressions should be used to find the length of the curve y=x^(2/3) from x=-1 to x=1?

 

a) 2*∫ sqrt(1+(9/4)y) dy from 0 to 1

 

b) ∫ sqrt(1+(9/4)y) dy from -1 to 1

 

c) ∫ sqrt(1+y^3) dy from 0 to 1

 

d) ∫ sqrt(1+y^6) dy from 0 to 1

 

e) ∫ sqrt(1+y^(9/4)) dy from 0 to 1

 

Answer: A

 

Please show all your work.

 

 

Answer 1

If you graph y=x^(2/3) on a graphing utility you'll see a cusp at (0,0). So you might have problems integrating over it.

 

Also the graph is symmetric with respect to the y-axis.

 

So A seems the safe choice.