Hello, I can't figure this one out. Can someone please help me with this problem?
Evaluate the integral
along the stated curve
a.) y = sin((pi*x)/2) from (0,0) to (1,1)
b.) x = y^3 from (0,0) to (1,1)
See attachment for details of integration.
To answer your second question have you studied Path Independence Yet?
Let the field be F = f i + g j
if df/dy = dg/dx F is the gradient of a scalar function phi.
The line integral is then simply phi(endpoint) - phi(initialpoint)
If you haven't studied this you will including how to find phi -- note for the phi I gave grad(phi) = F
and phi(1,1)- phi(0,0) = 3
For a complete discussion of path independence and conservative fields
see my web site Line Integrals