Purchase Solution

# Green's theorem

Not what you're looking for?

Apply Green's Theorem to evaluate the integral over C of 2(x^2+y^2)dx + (x+y)^2 dy, where C is the boundary of the triangle with vertices (1,1), (2,2) and (1,3) oriented in the counterclockwise direction.

Also check the result by direct integration.

Please show detailed working so I can follow the steps of the working.

Thank you

##### Solution Summary

This shows how to use Green's theorem to evaluate an integral. The triangle vertices oriented in the counterclockwise directions are given.

##### Solution Preview

Please see the attached doc files

First we use the Green's Theorem in the plane:
The closed surface is:

We consider:

Then :

which is:

on the given surface. We can divide ...

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.