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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 r=cos2胃

Short Answer

Expert verified

The area bounded by one petal is蟺8unit2

Step by step solution

01

Given information

The curve isr=cos2胃

02

Area

The area bounded by the curve is,

A=12鈭�伪尾r2d胃A=12鈭�0蟺4cos2胃2d胃A=12鈭�0蟺4cos22胃d胃A=12鈭�0蟺41+cos4胃2d胃A=12胃+sin4胃40蟺4A=12蟺4+sin4蟺44-0A=蟺8unit2

The area isA=蟺8unit2

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Most popular questions from this chapter

Let A>B>0. Show that the distance from any point on the graph of the curve with equation x2A2+y2B2=1to the point (-C,0)isD2=A2+CxA2, whereC=A2-B2.

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.

r=sin2胃

Complete the definitions in Exercises3-5.

Given two points in a plane, called _______, an ellipse is the set of points in the plane for which _______.

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

directrixx=-1,focus(2,5)

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

directrixx=x0, focusx1,y1,wherex0鈮�x1.
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