# 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?

Apr 27, 2017

$R \approx .5909624501$

#### Explanation:

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

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 ():
${e}^{- {x}^{2}} = 1 - \cos x$
(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 $R$
$R = {\int}_{0}^{.94194} \left({e}^{- {x}^{2}}\right) - \left(1 - \cos x\right) \mathrm{dx}$

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