Integration by parts (2-x)cos(nPi/2)x?

In summary, the person is asking for help with understanding how to integrate (2-x)cos(nPi/2)x, (1,2) and is questioning whether (nPi/2) should be treated as a constant during integration. Another person responds that it is a constant and suggests integrating by parts, but asks for clarification on the function. The original person confirms the function and expresses confidence in being able to integrate it.
  • #1
Splint
10
0

Homework Statement


Hi,

I'm doing fouier transforms and I'm not sure how to integrate (2-x)cos(nPi/2)x, (1,2). Anyone able to help me out? Even the indefinite integral would be fine.

Homework Equations



The Attempt at a Solution


I guess u would be (2-x) and dv would be cos(nPi/2)x dx. I'm not sure how to handle (nPi/2) since it is not a constant. Does (nPi/2) stay with x at all times?

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
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  • #2
n pi/2 IS a constant during the integration with respect to x.
Yes, it will be fine if you integrate by parts. How is the function exactly defined? Are you sure that you wrote the cosine function correctly? .

ehild
 
Last edited:
  • #3
Thanks Ehild,

It's actually a half range expansion. The function is:

f(x)= (1, 0<x<1
(2-x, 1=<x=<2

So I believe the cosine function is correct. I won't try and integrate it right now but I should be ok with it.

Many thanks
Splint
 

FAQ: Integration by parts (2-x)cos(nPi/2)x?

What is Integration by Parts?

Integration by parts is a method in calculus used to find the integral of a product of two functions. It involves rewriting the integral in terms of a new function and its derivative.

How do you use Integration by Parts?

To use Integration by Parts, you need to identify two functions, u and v, in the integral. Then, you apply the formula: ∫u dv = uv - ∫v du. This allows you to rewrite the integral in a form that is easier to solve.

What is the purpose of (2-x)cos(nPi/2)x in Integration by Parts?

The purpose of (2-x)cos(nPi/2)x in Integration by Parts is to serve as the two functions, u and v, in the formula. The function u is (2-x) and the function v is cos(nPi/2)x. This allows you to rewrite the integral in terms of these two functions and their derivatives.

How do you choose which function to assign as u and v in Integration by Parts?

When choosing which function to assign as u and v in Integration by Parts, you should follow the acronym "LIATE", which stands for Logarithmic, Inverse Trigonometric, Algebraic, Trigonometric, and Exponential. The functions that come first in this list should be assigned as u, while the functions that come later should be assigned as v.

What is the final step in solving an integral using Integration by Parts?

The final step in solving an integral using Integration by Parts is to check your answer by differentiating it. If the result is the original integrand, then your solution is correct. If not, you may need to use Integration by Parts again or try a different method.

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