How to find the area above and area below with the equations:

Question

y = e^x + 2 and y = 3 - x?

Answer 1

Let y = f (x ) = e^x + 2 and y = g (x ) = 3 - x.

The area below the curves be the area bounded between the curves in the interval [-2 , 0].

And the area above the curves be the area bounded between the curves in the interval [0 , 2].

Formula for area bounded between the curves is as follows:

or

To find which function is greater, substiute x  value between the interval [-2 , 0]

Let us take x = -1.

f (x ) = e^x + 2 = e^-1 + 2 = 0.3678 + 2 = 3.3678.

g (x ) = 3 - (-1) = 3 + 1 = 4.

Therefore g (x ) > f (x ).

Area bounded below is 12.86466 square units.

 

Answer 2

To find which function is greater, substiute x  value between the interval [0 , 2]

Let us take x = 1.

f (x ) = e^x + 2 = e¹ + 2 = 2.71828 + 2 = 4.71828.

g (x ) = 3 - (1) = 3 -1 = 2.

Therefore f (x ) > g (x ).

Therefore area bounded above is 6.38906 square units and area bounded below is 12.86466 square units.