Chapter 9: Q. 33 (page 775)
Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by one petal of
Short Answer
The area bounded by one petal is
Chapter 9: Q. 33 (page 775)
Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by one petal of
The area bounded by one petal is
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Get started for freeUse Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
In Exercises 60 and 61 we ask you to prove Theorem 9.23 for ellipses and hyperbolas
Consider the ellipse with equation where . Let be the focus with coordinates . Let and l be the vertical line with equation . Show that for any point P on the ellipse, , where is the point on closest to .
In exercises 31-36 find a definite integral that represents the length of the specified polar curve, and then use a graphing calculator or computer algebra system to approximate the value of integral
In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.
Find a definite integral expression that represents the area of the given region in polar plane and then find the exact value of the expression
The region inside both of the cardioids
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