Sketch the region enclosed by the curves: y=e^(4x) , y=e^(8x) , and x=1. Decide whether to integrate with respect to xor y. Then find the area of the region.
2007-04-20 09:14:26 · 3 answers · asked by bhicks 1 in Science & Mathematics ➔ Mathematics
The area between these curves is fine to integrate with respect to x. The integral would be between 0 and 1 of:
⌡e^(8x) - e^(4x) dx
= 1/8 e^(8x) - 1/4 e^(4x)
from 0 to 1 --> 1/8 e^8 - 1/4 e^4 - 1/8 + 1/4
= 1/8 e^8 - 1/4 e^4 + 1/8
decimal approximation = 37.6 - 13.65 + .125 = 51.37
2007-04-20 09:27:03 · answer #1 · answered by Kathleen K 7 · 1⤊ 0⤋
A = ∫e^(8x).dx - ∫e^(4x).dx limits 0 to 1
A = (1/8).e^(8x) - (1/4).e^(4x)---lims. 0 to 1
A = [(1/8).e^8 - (1/4)e^4] - [1/8 - 1/4]
A = [372.3 - 13.6] + 0.125
A = 359 (to nearest whole number)
2007-04-20 10:25:25 · answer #2 · answered by Como 7 · 0⤊ 0⤋
to much calc cant handle it, need a calculator,.
2007-04-20 09:27:53 · answer #3 · answered by Luna_5 2 · 0⤊ 0⤋