Forgot my trig integral tricks

In summary, to remember trigonometric integral formulas, it is recommended to practice regularly and create reference materials. Tricks for solving tricky integrals include using identities, substitution, and integration by parts. To improve skills in solving integrals, practice and understanding of concepts is key. Common mistakes to avoid when solving integrals include using incorrect identities and not checking for accuracy. When approaching a challenging integral, breaking it down and using familiar patterns and graphs can help.
  • #1
pergradus
138
1

Homework Statement



∫[sin4(t)cos2(t) + cos4(t)sin2(t)]dt



The Attempt at a Solution



Is there any way to do this integral using a substitution, or do I need to just split it into two integrals and apply a very messy series of half-angle identities?

Thanks.
 
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  • #2
I would first factor cos(t)^2*sin(t)^2 out and look at what's left.
 
  • #3
DOH! That was stupid... finished. :)

Thanks a ton! BTW, this integral is involved in the area of a hypercycloid, which apparently is 3πa2/8.
 

FAQ: Forgot my trig integral tricks

How can I remember all the trigonometric integral formulas?

One of the best ways to remember trigonometric integral formulas is by practicing them regularly. You can also create flashcards or cheat sheets to refer to when needed. Additionally, understanding the basic concepts behind the formulas can also help in remembering them.

What are some common tricks for solving tricky trigonometric integrals?

Some common tricks for solving tricky trigonometric integrals include using trigonometric identities, substitution, and integration by parts. Practice and understanding the concepts behind these tricks will also help in solving trigonometric integrals more easily.

How can I improve my skills in solving trigonometric integrals?

Improving your skills in solving trigonometric integrals requires practice and understanding of the basic concepts. You can also attend workshops or online courses that specifically focus on trigonometric integrals to improve your skills.

What are some common mistakes to avoid when solving trigonometric integrals?

Some common mistakes to avoid when solving trigonometric integrals include forgetting to use the correct trigonometric identities, making calculation errors, and not checking the final answer for accuracy. It is also important to avoid memorizing the formulas without understanding the concepts behind them.

How can I approach a challenging trigonometric integral problem?

When faced with a challenging trigonometric integral problem, it is important to break it down into smaller, more manageable steps. Look for familiar patterns or trigonometric identities that can be used in the problem. It is also helpful to sketch a graph of the trigonometric function to visualize the problem and come up with a plan of attack.

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