Lucas is selling ribbons to raise money for the Juvenile Diabetes Research Foundation. His expenses include $23 for materials, p
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Answer:
This is the same as writing 7*Ln( e^(2x) + 10) + C
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Explanation:
Start with the equation
Apply the derivative and multiply both sides by 7 like so
The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)
This way we can do the following substitutions:
Integrating leads to
Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.
To verify the answer, you can apply the derivative to it and you should get back to the original integrand of
To solve this problem you must apply the proccedure shown below:
1. When you plot the given points, you obtain a trapezoid, therefore, you must apply the formula for calculate the area of a trapezoid, which is:
Where is the larger base,
is the smaller base and
is the height.
2. The dimensions are:
3. Substitute values:
The answer is: