How do I find the area of the region bounded by the curves y = e^x, y = e^-x, x= -2, and x = 1?
Even if you could just help me in getting started it would be a HUGE help.
Thanks!
did you make a sketch?
y = e^x and y = e^-x are reflections of each other in the y-axis, they intersect at (0,1)
x=-2 and x=1 are two vertical lines, thus forming two distinct "bounded" regions, one in the second quadrant and a smaller one of similar shape in the first quadrant.
So find the total area in two separate calculations.
the one in the first quadrant would be
∫(e^x - e^-x)dx from 0 to 1 and the larger one would be
∫(e^-x - e^x)dx from -2 to 0