- #1
Wormaldson
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Homework Statement
Find k such that the area between the function and the x-axis, bounded by x = 1 and x = k, is equal to 100 square units.
Homework Equations
y = 4e^(x/5)
The Attempt at a Solution
1. Wrote the problem as the definite integral from 1 to k of 4e^(x/5)dx = 100.
2. Antidifferentiated to obtain 20e^(x/5).
3. Made substitutions into F(b) - F(a) = 100 to obtain 20e^(k/5) - 20e^(1/5) = 100.
4. Solved for k and got k = 5*ln(5) + 1.
5. At that point I thought I had it all figured out, but when I did 20e^((5*ln(5) + 1)/5) - 20e^(1/5) to check I get 97.7122207 as the result. What am I doing wrong here? Any help would be appreciated.