Sophia_Calculus_I_FinalMilestone. Question and answers verified to pass

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22 questions were answered correctly. 3 questions were
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1


Find the following indefinite integral:




RATIONALE
First, make the substitution and find the differential:

, MILESTON
Solve for
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Replace with u and with :




Use the constant multiple rule:




Then, evaluate. Note: :




Simplify:




Back substitute :




CONCEPT
Changing the Variable: u-Substitution with
Trigonometric Functions



2


Determine if the requirements for Rolle’s theorem are met by
the function on the interval . If so, find

,the

, values of c in guaranteed by the
theorem.
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is a polynomial so it is 22/25
continuous on and

differentiable on . When
evaluated, and
. Therefore, and the
conditions of Rolle’s theorem
are met.

The value guaranteed by

Rolle's theorem is .



is a polynomial so it is
continuous on and
differentiable on .
When

and
evaluated,
. Therefore, and the
conditions of Rolle’s theorem
are met.

The value guaranteed by

Rolle's theorem is .



is a polynomial so it is
continuous on and
differentiable on .
When

evaluated, and .
Therefore, and the
conditions of Rolle’s Theorem
are not met.




is a polynomial so it is