Let R be the region in the first quadrant enclosed by the graphs of #y=e^(-x^2)#, #y=1-cosx#, and the y axis, how do you find the area of the region R?

1 Answer
Apr 27, 2017

Answer:

#R approx .5909624501#

Explanation:

I graphed the two functions and also roughly highlighted the area we are trying to calculate:
Screenshot from desmos

Overview: Find the integral from zero to first intersection point of the two functions of the upper function minus the lower function

To find intersection point: set two equations equal to each other and solve using calculator ():
#e^(-x^2)=1-cosx#
(On TI 83 to TI 84+CE: either use Numerical solver under MATH menu, or graph the functions and use intersect under CALC menu)

#x approx .94194#

Area of #R#
#R = int_0^(.94194)(e^(-x^2))-(1-cosx)dx#

Plug this into graphing calculator to get:
#R approx .5909624501#