Solving Improper Integral: 2-x^4 |U Substitution

[Mathematics07]

Homework Statement

The integral from -infinity to infinity of (2-x^4)dv

Homework Equations

U substitution

The Attempt at a Solution

Dont know what to use as my "u" ?



Can someone please help me out? Thank you in advance.

 

[n!kofeyn]

You have a dv in your given integral. Is this the integral you mean?
$$\int_{-\infty}^\infty (2-x^4) \,dx$$
If so, you do not need u-substitution here. Also, to compute an improper integral of this form you need to evaluate:
$$\lim_{s\to\infty} \int_{-s}^s (2-x^4) \,dx$$

 

[Mathematics07]

yes that the write integral . . so basically i just need to do regular anti derivate and then evaluate it ?

 

[Jay J]

$$\int_{-\infty}^\infty (2-x^4) \,dx$$
If so, you do not need u-substitution here. Also, to compute an improper integral of this form you need to evaluate:
$$\lim_{s\to\infty} \int_{-s}^s (2-x^4) \,dx$$

so for an example like this you would just do a regular anti derivative and then substitute your "s" in for the infinities and then evaluate >?

-Jay J-