Question
Find the trigonometric integral. (Use
for the constant of integration.)
Ask by Little Reid. in the United States
Mar 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The integral of
with respect to
is
.
Solution
Calculate the integral
.
Evaluate the integral by following steps:
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
- step1: Evaluate the integral:
- step2: Simplify the expression:
- step3: Add the constant of integral C:
The trigonometric integral ofis , where is the constant of integration.
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Bonus Knowledge
To solve the integral
, we can use integration by substitution.
Let
. Then, the derivative of
is:
Since
and
, we can rewrite our integral as follows:
This integral can be a bit complicated but an alternative way is to integrate by using the identity
and separate out parts of the integral:
Now let’s integrate by parts. Let
and
. This gives us:
The integration steps involve some manipulation which results in:
So the final result is:
Thus, the integral evaluates to: