2021-09-07

Calculus: Line Integrals

Jeffrey Jordon

Expert2021-10-20Added 2605 answers

Explanation

Line integrals can be used to evaluate integrals of two- or three-dimensional curves

The curve C is expressed by the following parametric equations given by

Thus, to evaluate the following integral given by

we use the following line integral formula given by

=

Since

We want to evaluate

Firstly, we must find the integrand

=

Also, the derivatives of

Since

Thus, using the line integral formula, we get

To evaluate the following integral

Let

Differentiable both sides of the following equation

Also, we have

Also, we find that the upper and lower limits of the integral must be

Thus, the line integral becomes

Thus, the following line integral implies that

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