Evaluate the line integral, where C is the given curve.
a) I =∫c y5ds, c:x = t4/4, y = t, 0 ≤ t ≤5
(i) Rewrite the integral in terms of t, i.e. I = få f(t) dt where
f(t) =
a =
b =
(b) Evaluate J= ∫c xy8ds C is the left half of the circle x² + y² = 4 traversed counter- clockwise. (1) Parameterise the circle using parameter t to measure the angle from the x- axis counter-clockwise.
x(t) =
y(t) =
(ii) Using that parameterisation, the integral can be written as J = ∫å g(t) dt, where:
a =
b =
g(t)=
(iii) Evaluate J
J =
