Are These Indefinite Integral Solutions Correct?

In summary: That's interesting. Anyway, in summary, the conversation is about someone asking for help verifying the correctness of their answers in some even integration problems. They provide four integration problems and their solutions, and another person confirms that they are all correct. The original poster apologizes for their post and explains their intentions, and the other person suggests using a Wolfram online integrator to check answers. The conversation ends with a mention of dimethyltryptamine and the original poster expressing gratitude for the link provided.
  • #1
DMT
9
0
Hey, I just need you guys to help verify that I got the correct answers on some of the even integration problems in my book. If one of them is incorrect, I'll post my work and hopefully can find out where I went wrong. Thanks!

1. [tex]\int[/tex] xcos(x[tex]^{2}[/tex])dx = [tex]\frac{1}{2}[/tex] sin(x[tex]^{2}[/tex]) +C

2. [tex]\int[/tex] x[tex]^{2}[/tex]cos(x)dx = x[tex]^{2}[/tex]sinx + 2xcosx - 2sinx + C

3. [tex]\int[/tex] x[tex]^{2}[/tex]e[tex]^{-x}[/tex]dx = -e[tex]^{-x}[/tex](x[tex]^{2}[/tex] +2x + 2) + C

4. [tex]\int[/tex] e[tex]^{x}[/tex]sinxdx = [tex]\frac{1}{2}[/tex](-e[tex]^{x}[/tex]cosx + e[tex]^{x}[/tex]sinx) + C
 
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  • #2
Hah! They are all right. Which probably suggests you are pretty good at what you are doing and don't really have a real "question". I'm not sure just checking homework answers is really what we're about here.
 
  • #3
Dick said:
Hah! They are all right. Which probably suggests you are pretty good at what you are doing and don't really have a real "question". I'm not sure just checking homework answers is really what we're about here.

Ok, sorry! I just wanted to make sure they were correct before I turned it in so my instructor wouldn't take off points. I'll keep my posts to HW help from now on. Though, if one of the answers ended up being incorrect, the post would have turned into a homework help post right away ;)
 
  • #4
http://en.wikipedia.org/wiki/Dimethyltryptamine" ??
 
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  • #5
VeeEight said:
http://en.wikipedia.org/wiki/Dimethyltryptamine" ??

fun stuff!
 
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  • #6
DMT said:
Ok, sorry! I just wanted to make sure they were correct before I turned it in so my instructor wouldn't take off points. I'll keep my posts to HW help from now on. Though, if one of the answers ended up being incorrect, the post would have turned into a homework help post right away ;)

Oh, that's ok. But there is no reason to post to HW help just to check answers to avoid point reductions. I think you should be genuinely confused before posting. Just my opinion.
 
  • #7
You can use the online integrator provided by Wolfram to check your answers.

http://integrals.wolfram.com/index.jsp

Also, you could just differentiate your result and see if you recover the integrand.
 
  • #8
vela said:
You can use the online integrator provided by Wolfram to check your answers.

http://integrals.wolfram.com/index.jsp

Also, you could just differentiate your result and see if you recover the integrand.

Wow! That is an amazing tool. Thanks for the link!
 

FAQ: Are These Indefinite Integral Solutions Correct?

What is an indefinite integral?

An indefinite integral is a mathematical concept used in calculus to find the general form of a function's antiderivative. It is often represented by the symbol ∫f(x)dx, where f(x) is the function being integrated and dx represents the variable of integration.

How is an indefinite integral different from a definite integral?

An indefinite integral does not have specific limits of integration, whereas a definite integral has both an upper and lower limit. This means that an indefinite integral yields a general solution, while a definite integral gives a specific numerical value.

What is the process for finding an indefinite integral?

The process for finding an indefinite integral involves using integration techniques, such as substitution, integration by parts, or trigonometric identities, to find the antiderivative of the function. The resulting antiderivative is the indefinite integral.

What is the relationship between derivatives and indefinite integrals?

The derivative and indefinite integral are inverse operations. This means that the derivative of an indefinite integral is equal to the original function, and the indefinite integral of a derivative is equal to the original function (up to a constant of integration).

How is the definite integral related to the area under a curve?

The definite integral can be used to find the area under a curve by calculating the signed area between the curve and the x-axis within a specified interval. This is known as the Fundamental Theorem of Calculus, which states that the definite integral is the reverse process of finding the area under a curve using integration.

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