Please show your work.Oalvarez said:1. I need help solving this integral, I've tried using trig substitution, but I'm getting nowhere with it.
∫x/(6x-x^2)^3/2dx
Like I said before, I tried changing the bottom to a radical and trig substituting but it doesn't seem to get me anywhere. Thanks in advanced for any help.
The process for solving integrals involves using techniques such as substitution, integration by parts, and trigonometric identities to simplify and then evaluate the integral.
The limits of integration are determined by the given problem or context. They can represent the bounds of a specific region on a graph or the beginning and end points of a function.
The power rule for integration states that the integral of x^n is equal to (x^(n+1))/(n+1) + C, where C is a constant. This rule is used when the integrand is a polynomial function.
Improper integrals are solved by breaking them into smaller integrals and evaluating each part separately. The improper integral may converge or diverge, depending on the behavior of the function at the limits of integration.
Yes, for the function ∫x/(6x-x^2)^3/2dx, we can use the substitution u = 6x-x^2 and du = (6-2x)dx to simplify the integral to ∫du/u^3/2, which can then be evaluated using the power rule for integration. The final result would be -(6x-x^2)^1/2 + C.