What is the Integral of x^2 sin pi x?

  • Thread starter Thread starter MillerGenuine
  • Start date Start date
  • Tags Tags
    Integral Pi Sin
Click For Summary
To solve the integral of x^2 sin(πx), integration by parts is required, and it must be applied twice. The polynomial component decreases in degree with each differentiation, while the trigonometric part remains. Eventually, this process leads to the integral of sin(πx). The solution involves careful selection of u and dv during integration by parts. Mastering this technique is essential for tackling similar problems effectively.
MillerGenuine
Messages
64
Reaction score
0
My calc is a bit rusty & i can not solve this problem for the life of me.
its the integral of x^2sin pi x.
I know you must integrate by parts..& i am have tried using both x^2 and sin pi x as my u.
Any help?
time is of the essence.


 
Physics news on Phys.org
You have to integrate by parts twice. The trig part doesn't go away, but the polynomial part will go down in degree every time you differentiate it until you're just left with the integral of sin x.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Calculating radius of gyration of plane figure about x-axis
  • · Replies 5 ·
Replies
5
Views
2K
Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
  • · Replies 3 ·
Replies
3
Views
2K
The integral of (sin x + arctan x)/x^2 diverges over (0,∞)
  • · Replies 5 ·
Replies
5
Views
2K
Laplace transform of ##f(t)=(u(t)-u(t-2\pi))\sin{t}##
  • · Replies 1 ·
Replies
1
Views
964
Area surface of revolution (rotating this astroid curve around the x-axis)
  • · Replies 2 ·
Replies
2
Views
2K
Line Integral of circle in counterclockwise direction
  • · Replies 5 ·
Replies
5
Views
2K
Why does dividing by ##\sin^2 x## solve the integral?
  • · Replies 27 ·
Replies
27
Views
4K
Curve for a line integral - direction confusion
  • · Replies 9 ·
Replies
9
Views
1K
Double Integral of function in region bounded by two circles
  • · Replies 19 ·
Replies
19
Views
2K
Prove that the integral is equal to ##\pi^2/8##
  • · Replies 105 ·
4
Replies
105
Views
6K