Integrating Sinx/x^2 from Y=4 to Y=0 with x=2 and x=√y

  • Thread starter theaviator
  • Start date
In summary, the conversation discusses finding an integral table for the function \int \frac{sin\,x}{x^2}\,dx or solving it by expanding sin x as an infinite series and dividing by x^2. The final answer is found to be 1-cos2, which is determined to be correct.
  • #1
theaviator
6
0
Y=4 x=2
∫ ∫ Sinx ∕ x^2 dx dy
Y=0 x=√y
 
Physics news on Phys.org
  • #2
Can one find an integral table with

[tex] \int \frac{sin\,x}{x^2}\,dx [/tex] ?

Alternatively, expand sin x as an infinite series, divide by x2 and solve for each term.
 
  • #3
i changed the order of the integration...the final answer i had is the same one in the sheet from which i get the problem...but i don't know id the way i solved it is right or wrong...please HELP...
X=2 y=x^2
∫ ∫ sinx/x^2 dx dy
X=0 y=0

X=2 y=x^2
= ∫ [(sinx/x^2)y] dx
X=0 y=0

X=2
=∫ sinx dx
X=0
X=2
= [ -cosx]
X=0

= -cos2+cos(0)= 1-cos2
 
  • #4
That is correct.
 

What does it mean to integrate Sinx/x^2 from Y=4 to Y=0 with x=2 and x=√y?

Integrating Sinx/x^2 from Y=4 to Y=0 with x=2 and x=√y means finding the area under the curve of the function Sinx/x^2 within the given boundaries of Y=4 and Y=0, with x values ranging from 2 to √y.

Why is this type of integration important?

This type of integration is important because it allows us to calculate the total area under a curve, which has many real-world applications such as calculating velocity, distance, and displacement.

What is the general process for integrating a function?

The general process for integrating a function involves finding the anti-derivative of the function, then applying the boundaries to calculate the definite integral.

What is the significance of using a definite integral in this problem?

Using a definite integral in this problem allows us to find the exact value of the area under the curve within the given boundaries, as opposed to an indefinite integral which gives us a general function.

How can the result of this integration be interpreted?

The result of this integration can be interpreted as the total area under the curve of the function Sinx/x^2 between the boundaries of Y=4 and Y=0, with x values ranging from 2 to √y. It can also be interpreted as the exact value of the integral of the function within these boundaries.

Similar threads

  • Calculus and Beyond Homework Help
Replies
10
Views
446
  • Calculus and Beyond Homework Help
Replies
20
Views
437
  • Calculus and Beyond Homework Help
Replies
2
Views
512
  • Calculus and Beyond Homework Help
Replies
3
Views
584
  • Calculus and Beyond Homework Help
Replies
2
Views
544
  • Calculus and Beyond Homework Help
Replies
14
Views
249
  • Calculus and Beyond Homework Help
Replies
6
Views
760
  • Calculus and Beyond Homework Help
Replies
7
Views
688
  • Calculus and Beyond Homework Help
Replies
13
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
346
Back
Top