Q. 39 - Calculus

Question

Each of the integral in exercise 38-44 represents the area of a region in a plane use polar coordinates to sketch the region and evaluate the expression 

The integral is ${\int }_0^{\pi }{(1+\cos \theta )}^{2}d\theta$

Step-by-Step Solution

Answer

The area can be given as 4.71 units

The graph can be given as 

Step 1: Given information

We are given an integral as ${\int }_0^{\pi }{(1+\cos \theta )}^{2}d\theta$

Step 2: Sketch the graph

On comparing with standard equation we get $r=1+\cos \theta$

Now using graphing utility we have,

Step 3: Evaluate

We have,

$$\begin{gathered} {\int }_0^{\pi }{(1+\cos \theta )}^{2}d\theta \\ U\sin g CAS system we get, \\ A=4.71units \end{gathered}$$