The area of thee region enclosed by the graph of the polar curve `r=(1)/(sintheta+costheta)` and the x- and y-axis is

Options

A. 0.48
B. 0.5
C. 0.52
D. 0.98

Answer

B

Explanation

With your calculator in polar mode, graph `r=(1)/(sintheta+costheta)` in a [-3,3] by [-3,3] window. Let `theta` run from 0 to `2pi` in increments of 0.1. the graph of the function and the two axes form an isosceles right triangle of side length 1, so its area is 0.5.
An alternative solution is to multiply both sides of the equation by `sintheta+costheta` to get `rsintheta+rcostheta=1`. since x=r`costheta and y=rsintheta`, the rectangular form of the equation is x+y=1. this line makes an isosceles right triangle of unit leg lengths with the axes, the area of which is `(1)/(2)(1)(1)=0.5`.