Posted by Sean on Thursday, March 13, 2008 at 2:43pm.
What is the indefinite integral of:
If I could have two things given to me please, I'd be grateful. The two things are:
1) Trick/Technique to Use
2) First 2 or 3 steps
Thanks in advanced.
- Calculus III - Count Iblis, Thursday, March 13, 2008 at 5:58pm
Express sin(3x) in terms of sin(x).
exp(ix) = cos(x) + i sin(x) (1)
Take the third power of both sides:
exp(3ix) = [cos(x) + i sin(x)]^3
From (1) it follows that the imaginary part of the left hand side is sin(3x)
Expand the right hand side and take the imaginary part. You then find:
sin(3x) = -sin^3(x) + 3sin(x)cos^2(x)
= 3 sin(x) - 4 sin^3(x)
It then follws that:
3 - 4 sin^2(x)
which is almost trivial to integrate.
- Calculus III - Sean, Thursday, March 13, 2008 at 7:01pm
Out of curiosity, where did the 'i' come from, and what technique did you use?
Also, how did you write sin(3x) In terms of sin(x)?
Answer this Question
More Related Questions
- Calculus II - 1) Compute the indefinite integral: integral 2x ln(x^2 - 8x + 18) ...
- Calculus - I have two questions, because I'm preparing for a math test on monday...
- Math - 1. Evaluate the indefinite integral ([6x^2 + 12x^(3/2) +4x+9]/sqrt x)dx. ...
- Calc BC - 1. Find the indefinite integral. Indefinite integral tan^3(pix/7)sec^2...
- Calculus - Solve these indefinite and definite integrals. [integration sign] 4j-...
- Calculus II/III - A. Find the integral of the following function. Integral of (x...
- Math - good day please help with this indefinite integral,especially what ...
- Calculus - Would someone please tell me how to solve these two problems? Find ...
- Calculus - Hello Everyone, I need help with Calc II. 1. Integral from 0 to 1 of...
- Calculus Please Help - Evaluate the indefinite integral Note: Use an upper-case...