- #1
bobsmith76
- 336
- 0
Homework Statement
I don't understand why the x/2 is not being integrated. I would think one should use u substitution. u = x/2, du = x, but they're not doing that.
Integrating x/2: Why is u-substitution not being used?
- Thread starter bobsmith76
- Start date
-
- Tags
- Integration Trigonometric
In summary, trigonometric integration is the process of finding the integral of a function that contains trigonometric functions. It is important because it allows us to solve a wide variety of mathematical problems and has many practical applications. The basic trigonometric integration rules include the power rule, product rule, quotient rule, and chain rule. To solve a trigonometric integral, one should identify the type of integral and use the appropriate integration rule, as well as techniques such as substitution, integration by parts, or trigonometric identities. Common mistakes when integrating trigonometric functions include missing negative signs, using incorrect identities, and forgetting to add a constant of integration. Careful checking and using the correct rules and techniques can help avoid these mistakes.
I don't understand why the x/2 is not being integrated. I would think one should use u substitution. u = x/2, du = x, but they're not doing that.
- #2
abhinav111
- 3
- 0
Actually the book referred has used this substitution and have finally put u=x/2 again as question is asked in form of x/2 and not in u.
- #3
Char. Limit
Gold Member
- 1,222
- 22
Actually, they DID, but they skipped a couple of steps (like explaining HOW they integrated). If you try a u-substitution, you'll get the same answer they did.
Related to Integrating x/2: Why is u-substitution not being used?
1. What is trigonometric integration?
Trigonometric integration is a method used in calculus to find the integral of a function that contains trigonometric functions, such as sine, cosine, and tangent.
2. How is trigonometric integration different from regular integration?
Trigonometric integration involves using specific trigonometric identities and substitution techniques to simplify the integral and solve it. Regular integration involves finding the antiderivative of a function using basic integration rules.
3. What are some common trigonometric identities used in trigonometric integration?
Some common trigonometric identities used in trigonometric integration include the double angle formula, half angle formula, and Pythagorean identities. These identities help to simplify and solve the integral.
4. Can trigonometric integration be used for all types of trigonometric functions?
Yes, trigonometric integration can be used for all types of trigonometric functions, including inverse trigonometric functions such as arcsine, arccosine, and arctangent.
5. What are some real-world applications of trigonometric integration?
Trigonometric integration is commonly used in physics, engineering, and other scientific fields to solve problems involving periodic motion, such as the motion of a pendulum or a vibrating string. It is also used in signal processing and electrical engineering to analyze and manipulate trigonometric waveforms.
Similar threads
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help