# How do you find the area of the region bounded by the given curves #y = 6x^2lnx # and #y = 24lnx#?

First set the equations equal to each other, and find the intersection points, then find the area between the curves.

By setting the equations equal to each other, I found that the functions intersect at

Focus on the unbounded (indefinite) integral to solve:

Use integration by parts:

Now go back to the definite integral:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the area of the region bounded by the given curves y = 6x^2lnx and y = 24lnx, you need to first determine the points of intersection of these curves. Then, integrate the absolute difference of the two functions between these points of intersection. The points of intersection can be found by solving the equation 6x^2lnx = 24lnx. After finding the points of intersection, integrate |6x^2lnx - 24lnx| with respect to x over the appropriate interval.

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7