Concept explainers
To graph: The given polar curve. Also, find the area enclosed the curve and find the slope of the curve at the point where
Answer to Problem 59E
The required the area enclosed the curve and the slope of the curve at the point where
Explanation of Solution
Given information:
The polar curve:
Calculation:
The given curve is
It is known that in a polar
The graph of the given curve is shown below:
It is seen that the shaded region between the curves lie within the interval
Write the area of the given region as:
Simplify the above expression further.
Thus, the area of the region is
Now, it is known that in a polar coordinate system, if
Rewrite x and y as:
And,
Since, polar curves lie in xy -plane; so, the slope of the polar curve and the slope of the tangent are same that is,
The slope can be written as:
Now, write the slope at
Hence, the required the area enclosed the curve and the slope of the curve at the point where
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic
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