Calculus Question Help please!--Question fixed?

Question

Approximate the area under the graph of, f(x)= e^(x/3) + 2. From x=0 to x=3 and above the x-axis using the left endpoints with n=4. Round the answer to two decimal place

Answer 1

You are supposed to approximate the area using rectangles. n = 4 usually means they want you to use 4 rectangles. But in this case, since the size of the interval is 3, they may just want 3 rectangles and the 4 comes from the 4 x values that define the left and right sides of the rectangles.
Divide the interval (0, 3) into 3 even intervals. Use the value of f(x) at the left side of each interval to determine the height of each rectangle. Add the area of all the rectangles to get your area estimate.

Answer 2

Area
= ∫ [e^(x/3) + 2] dx ( x=0 to x=3)
= 3e^(x/3) + 2x ( x=0 to x=3)
= 3e^(3/3) + 2(3) - 3e^(0) - 2(0)
= 3e + 6 - 3
= 3 (e + 1)
= 11.15

The approximate method to be used as explained by demiurge42 is as under.

x= 0 => f(x) = e^0 + 2 = 3.0000
x=1 => f(x) = e^(1/3) + 2 = 3.3955
x=2 => f(x) = e^(2/3) + 2 = 3.9478

Area = (1/3)(3 - 0)( 3.0000 + 3.3955 + 3.9478)
= 10.34