SOLUTION: The Question: Find the area bounded by 1-e^(-2x) in the interval x = -1 to x = 1. Thank-you for your assistance.

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Question 398002: The Question:
Find the area bounded by 1-e^(-2x) in the interval x = -1 to x = 1.
Thank-you for your assistance.
Found 2 solutions by Alan3354, richard1234:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I did this earlier today.
The integral = x + (e^-2x)/2

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+1+-+e%5E%28-2x%29%29

The area is normally given by int%28%281+-+e%5E%28-2x%29%29%2C+dx%2C+-1%2C+1%29. However, part of the area is counted as negative, so we must put a negative wherever 1+-+e%5E%28-2x%29+%3C+0.

The function goes below the x-axis when x+%3C+0, so I'll split into two integrals:

(There'll be lots of negative signs involved so I just rewrote the first integral)

To evaluate the indefinite integral int%28%281-e%5E%28-2x%29%29%2C+dx%29, begin with the substitution u+=+-2x, du+=+-2dx. Replacing dx, we obtain



I'll let you finish off the problem by evaluating at the bounds (the rest is just arithmetic and applying the fundamental theorem of calculus).