javacola said:Homework Statement
1~~0 (x^7)/sqrt(4-3x^16) dx
The Attempt at a Solution
There really isn't one. I am as clueless as one can get in calculus. I know that I am supposed to substitute the variable "u" in for a section of this problem, but really don't know anything after that. I understand derivatives but that is about it. If someone could walk me through this problem it'd be great.
LCKurtz said:You know that when you make a u substitution, you need the du to be in the integral. You have x7 sitting there. What u might give you an x7 in the du? Think about that.
LCKurtz said:You know that when you make a u substitution, you need the du to be in the integral. You have x7 sitting there. What u might give you an x7 in the du? Think about that.
javacola said:7x^6?
LCKurtz said:No, you are just guessing. If you want to get x7 in the answer for du, what must u be? You got x6 in your answer, not x7. C'mon, you can do better than that.
U-substitution is a method used in calculus to simplify the integration of functions that can be written in the form of a chain rule. It involves substituting a variable, typically denoted as "u", for a more complex expression within the integrand.
The key to choosing the appropriate "u" for a u-substitution problem is to identify which part of the integrand is causing the complexity. This part should be substituted with "u" so that the remaining expression can be simplified and easily integrated.
No, u-substitution can only be used for integration problems that involve a chain rule. It cannot be used for problems that involve trigonometric functions or logarithmic functions, for example.
Yes, some common mistakes to avoid when using u-substitution include forgetting to change the limits of integration when substituting for "u", incorrectly choosing "u" as a constant rather than a variable, and not simplifying the remaining expression before integrating.
To check if your u-substitution is correct, you can differentiate the final result and see if it matches the original integrand. If it does, then your substitution was successful. You can also plug in the original expression for "u" and see if it simplifies to the original integrand.