Question
What is the area of the region bounded by the graphs y=e^x, y=1, x=-1?
Answers
Reiny
I see a thin "triangular" region in quadrant II
form x = -1 to x=0
the "height" is 1 - e^x
area = ∫(1 - e^x) dx from -1 to 0
= [ x - e^x] from -1 to 0
= 0 - 1 - (-1 - e^-1)
= e^-1
or
= 1/e
form x = -1 to x=0
the "height" is 1 - e^x
area = ∫(1 - e^x) dx from -1 to 0
= [ x - e^x] from -1 to 0
= 0 - 1 - (-1 - e^-1)
= e^-1
or
= 1/e