Help Me Integrate sin2(x): Tips & Tricks

• v0id19
In summary, the best way to approach integrating sin2(x) is by using the trigonometric identity sin2(x) = 2sin(x)cos(x). Substitution can also be used, with a common substitution being u = sin(x). There are also special techniques such as the power-reducing formula and the half-angle formula. To check the correctness of the integration, one can differentiate the answer and compare it to the original function. Tips for solving tricky integrals involving sin2(x) include using integration by parts, breaking up the integral into smaller parts, and looking for possible substitutions.
v0id19

Homework Statement

For whatever reason, I'm having issues integrating sin2(x)

Homework Equations

I can use U-sub, trig-sub, integration by parts, partial fractions, in any combination as needed

The Attempt at a Solution

My brain is failing me, so any hints would be awesome.

Last edited:

Use a double angle formula for the last one. cos(2x)=?

i have that in my table of integrals in the back of my calc book. That's where i'd look. heh

sweet it worked :D
thanks a bunch

What is the best way to approach integrating sin2(x)?

The best way to integrate sin2(x) is by using the trigonometric identity: sin2(x) = 2sin(x)cos(x). This will help simplify the integration process.

Can I use substitution to integrate sin2(x)?

Yes, you can use substitution to integrate sin2(x). A common substitution is u = sin(x), which results in the integral becoming 2u(1-u^2)du.

Are there any special techniques for integrating sin2(x)?

Yes, there are a few special techniques that can be used to integrate sin2(x). These include using the power-reducing formula: sin2(x) = 1/2 - 1/2cos(2x), or using the half-angle formula: sin2(x) = 1/2sin(x/2)cos(x/2).

How can I check if my integration of sin2(x) is correct?

One way to check if your integration of sin2(x) is correct is by differentiating your answer. Your result should be equal to the original function, sin2(x). If it is not, then you may have made a mistake during integration.

Are there any tips for solving tricky integrals involving sin2(x)?

Yes, one tip is to try using integration by parts. Another tip is to break up the integral into smaller parts and use trigonometric identities to simplify each part. Also, make sure to check for any possible substitutions that can make the integration process easier.

• Calculus and Beyond Homework Help
Replies
22
Views
2K
• Calculus and Beyond Homework Help
Replies
44
Views
4K
• Calculus and Beyond Homework Help
Replies
10
Views
1K
• Calculus and Beyond Homework Help
Replies
4
Views
1K
• Calculus and Beyond Homework Help
Replies
18
Views
3K
• Calculus and Beyond Homework Help
Replies
4
Views
1K
• Calculus and Beyond Homework Help
Replies
14
Views
1K
• Calculus and Beyond Homework Help
Replies
8
Views
1K
• Calculus and Beyond Homework Help
Replies
12
Views
3K
• Calculus and Beyond Homework Help
Replies
3
Views
1K