Evaluate the line integral, where C is the given curve.
1. ∫C y ds, C: x = t2, y = 2t, 0 ⩽ t ⩽ 3
To Evaluate: The line integral for a curve .
The parametric equations of curve and its limits are given as follows.
Write the expression to evaluate the line integral for a function along the curve .
is the lower limit of the curve and
is the upper limit of the curve .
Write the required differential and integration formulae to evaluate the given integral.
Evaluation of line integral :
Substitute for , for , for , for , 0 for , and 3 for in equation (1),
Rewrite and compute the expression as follows.
Simplify the expression as follows
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