MHB How Can I Integrate x*sqrt(1-x^4) Using Trig Substitution?

Click For Summary
To integrate x*sqrt(1-x^4), the suggested substitution is u = x^2, leading to du = 2x dx. This transforms the integral into (1/2)∫sqrt(1-u^2) du. A further trigonometric substitution of u = sin(w) is recommended for simplification. The discussion confirms the validity of this approach and expresses readiness to proceed with the integration.
annie122
Messages
51
Reaction score
0
how do i go about integrating

x*sqrt(1-x^4)??

i have no idea
 
Physics news on Phys.org
Re: another trig substitution

Yuuki said:
how do i go about integrating

$$\int x \cdot \sqrt{1-x^4}dx$$

i have no idea

I would let $$u = x^2 \therefore du = 2x dx$$

$$\int x \cdot \sqrt{1-x^4} \cdot \dfrac{du}{2x} = \dfrac{1}{2} \int \sqrt{1-u^2} du$$

Do you know a trig sub for this integral?
 
Re: another trig substitution

u = sin(w) right?

thx!
 
Re: another trig substitution

Yuuki said:
u = sin(w) right?

thx!

Yes, that's the right sub to use. Are you ok going forward?
 
yup thank you
 
Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
View full post »

Similar threads

I Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
2K
B Integration by parts of inverse sine, a solved exercise, some doubts...
  • · Replies 4 ·
Replies
4
Views
3K
MHB How to Evaluate the Integral of an Even Trig Function in a Radical?
  • · Replies 9 ·
Replies
9
Views
1K
I Substitution in a definite integral
  • · Replies 6 ·
Replies
6
Views
3K
I Integration Using Trigonometric Substitution
  • · Replies 8 ·
Replies
8
Views
2K
MHB 7.3.5 Integral with trig substitution
  • · Replies 1 ·
Replies
1
Views
2K
MHB Integral using trig substitution
  • · Replies 1 ·
Replies
1
Views
1K
I What's my mistake in this integration problem?
  • · Replies 8 ·
Replies
8
Views
3K
MHB Integral using trig substitution
  • · Replies 5 ·
Replies
5
Views
2K
B Trigonometric substitution, a case I'd like to share
  • · Replies 3 ·
Replies
3
Views
3K