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Example Questions
Example Question #801 : Ap Calculus Ab
Evaluate the integral
To evaluate this integral, we must first rewrite the from the denominator, as a
in the numerator. This gives us
Since the has an exponent, we will pick it for our u-substitution.
Now we find by differentiating.
This gives us the cosine piece. Writing everything in terms or u, we get
To integrate this we use the following basic integral form:
Applying this to our integral, we get
Now we can "un-substitute" to get back to x-terms. Replacing with
, we get
Now we use the 2nd Fundamental Theorem of Calculus. We plug in the upper bound of , then plug in the lower bound of
, and subtract.
Doing this we get
This is the correct answer.
Example Question #1 : Basic Properties Of Definite Integrals (Additivity And Linearity)
If are continuous functions,
,
, and
, find
.
Not enough information
We proceed as follows
. (Start)
. (Break up the integral using the additive rule.)
. (We don't have information about the 2nd integral, so we solve our first equation for
and replace it in this integral.)
. (Factor out the
using linearity.)
. (Substitute in what we were given.)
.
Example Question #1 : Basic Properties Of Definite Integrals (Additivity And Linearity)
Example Question #1 : Basic Properties Of Definite Integrals (Additivity And Linearity)
Example Question #1 : Basic Properties Of Definite Integrals (Additivity And Linearity)
Example Question #1 : Basic Properties Of Definite Integrals (Additivity And Linearity)
Example Question #1 : Basic Properties Of Definite Integrals (Additivity And Linearity)
Example Question #1 : Basic Properties Of Definite Integrals (Additivity And Linearity)
Example Question #5 : Basic Properties Of Definite Integrals (Additivity And Linearity)
Example Question #33 : Interpretations And Properties Of Definite Integrals
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