Integral by substitution trigonometric ? a- ) int x/sqrt(9-x²)
I can not completely resolve this issue, please someone give me a hint how to solve!
I can not completely resolve this issue, please someone give me a hint how to solve!
2 Answers
Explanation:
So, we want
In general, if we encounter an integral with the root
(We could use cosine, but using sine avoids unnecessary negative signs popping up.)
Here,
Rewrite with the substitution:
Simplify:
Recall the identity
This tells us that
We need to go back to
So, our integral becomes
Explanation:
The question is to evaluate:
Draw a right-angle triangle with an angle
Label the side opposite
Label the hypotenuse as
Now examine the triangle and notice that
Also notice that the side of the triangle adjacent to
Now rewrite the integral in terms of
Now simplify:
Now put the expression back in terms of