Find the integral x^3 sqrt(x^2 + x^8 + 8) cos x dx

It's a definite integral, so you can use the properties of integrals to simplify the problem.In summary, the conversation discusses finding the integral of the function f(x) = x^3 sqrt(x^2 + x^8 + 8) cox(x) dx. The problem involves either integration by parts or substitution, but finding an antiderivative may be difficult. It is mentioned that the integral is a definite integral evaluated from -14 to 14, and the fact that the function is odd can be used to simplify the problem. The conversation concludes by discussing the properties of integrals and how they can be used to simplify the problem further.
  • #1
golb0016
16
0

Homework Statement


Find the integral

f(x) = x^3 sqrt(x^2 + x^8 + 8) cox(x) dx


The Attempt at a Solution



I need help starting. It appears to be either integration by parts and/or substituion.
 
Physics news on Phys.org
  • #2


You are going to have a tough time finding an antiderivative for that. Is it actually a definite integral?
 
  • #3


The problem wanted the function evaluated from -14 to 14. Does it make a difference if it is definitive or not? Is there a trick if it is definitive?
 
  • #4


golb0016 said:
The problem wanted the function evaluated from -14 to 14. Does it make a difference if it is definitive or not? Is there a trick if it is definitive?

It does in this case. For your function f(-x)=(-f(x)), it's an odd function. What happens if you integrate an odd function over a symmetric interval around the origin?
 
  • #5


Does the positive and negative parts cancel out if it is symmetric?
 
  • #6


golb0016 said:
Does the positive and negative parts cancel out if it is symmetric?

That's the idea.
 

1. What is the process for finding the integral of this equation?

The process for finding the integral of x^3 sqrt(x^2 + x^8 + 8) cos x dx would involve using integration techniques such as substitution or integration by parts.

2. How do you handle the x^3 term in the equation?

The x^3 term can be handled by using integration by parts, setting u = x^3 and dv = sqrt(x^2 + x^8 + 8) cos x dx.

3. Can this integral be solved using only substitution?

In this particular equation, it would not be possible to solve using only substitution as it would result in a more complex integral that cannot be easily solved.

4. What is the significance of the cos x term in the equation?

The cos x term represents the cosine function, which is a trigonometric function commonly used in mathematical equations. In this particular equation, it appears because of the use of integration by parts.

5. Is there a specific range of values for x that this integral is valid for?

This integral can be solved for any real values of x, as long as the function remains continuous and differentiable in the given range.

Similar threads

Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
    • Calculus and Beyond Homework Help
Replies
3
Views
341
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
    • Calculus and Beyond Homework Help
Replies
7
Views
702
Centroid calculation using integrals
    • Calculus and Beyond Homework Help
Replies
9
Views
756
Differentiate the given integral
    • Calculus and Beyond Homework Help
Replies
15
Views
783
Integrals that keep me up at night
    • Calculus and Beyond Homework Help
Replies
22
Views
1K
Can a human calculate this without a calculator?
    • Calculus and Beyond Homework Help
Replies
11
Views
694
Improper integral of a normal function
    • Calculus and Beyond Homework Help
Replies
7
Views
933
Line Integral of circle in counterclockwise direction
    • Calculus and Beyond Homework Help
Replies
5
Views
681
Integration problem using inscribed rectangles
    • Calculus and Beyond Homework Help
Replies
14
Views
235
Find the equation of the tangent in the given problem
    • Calculus and Beyond Homework Help
Replies
4
Views
807

Hot Threads

Recent Insights

Back
Top