Integration Problem involving absolute bracket, sine,cosine

In summary, an integration problem involving absolute bracket, sine, and cosine is a mathematical problem that requires finding the value of an indefinite integral that contains absolute values and trigonometric functions. To solve this type of problem, you can use the properties of absolute values and the trigonometric identities for sine and cosine, as well as techniques such as substitution and integration by parts. Multiple solutions are possible for these problems due to the multiple values that can satisfy the given equation. To check if your solution is correct, you can take the derivative and compare it to the original integrand.
  • #1
appplejack
43
0

Homework Statement


Evaluate

∫(1)to(-1) l sin(x) l dx


Homework Equations





The Attempt at a Solution



If I just leave it like this, is it wrong?

1. ∫(1)to(-1) l sin(x) l dx = l -cos (x)l

2. l -cos (1) l — l -cos (-1)l = 0 - 0 = 0
 
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  • #2
Way wrong. Split the integral up into regions where sin(x) has a definite sign. Work the integral out on each of those regions. Then add them up. You'll get a very different answer.
 
Last edited:

Related to Integration Problem involving absolute bracket, sine,cosine

1. What is an integration problem involving absolute bracket, sine, and cosine?

An integration problem involving absolute bracket, sine, and cosine is a mathematical problem that requires finding the value of an indefinite integral that contains absolute values and trigonometric functions.

2. How do I solve an integration problem involving absolute bracket, sine, and cosine?

To solve an integration problem involving absolute bracket, sine, and cosine, you can use the properties of absolute values and the trigonometric identities for sine and cosine. You can also use substitution or integration by parts to simplify the integral.

3. What are the common techniques used to solve an integration problem with absolute bracket, sine, and cosine?

The common techniques used to solve an integration problem with absolute bracket, sine, and cosine include using the properties of absolute values, trigonometric identities, substitution, and integration by parts. These techniques help simplify the integral and make it easier to solve.

4. Can an integration problem involving absolute bracket, sine, and cosine have multiple solutions?

Yes, an integration problem involving absolute bracket, sine, and cosine can have multiple solutions. This is because the absolute values and trigonometric functions can have multiple values that satisfy the given equation.

5. How can I check if my solution to an integration problem with absolute bracket, sine, and cosine is correct?

You can check if your solution to an integration problem with absolute bracket, sine, and cosine is correct by taking the derivative of your solution and comparing it to the original integrand. If the derivative matches the original integrand, then your solution is correct.

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