trigonometric substitution

User Generated

lvyral93

Mathematics

Question Description

Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service.

Explanation & Answer

Thank you for the opportunity to help you with your question!

Dividing both sides of the initial equation by 3x and multiplying both sides by dx gives the equation:

dy = (sqrt(x^2-25)/(3x))dx

This equation can be integrated leaving the equation:

y = (1/9)(sqrt(x^2-25)^(3/2)) + C.

Plugging in the point (5,3) means C = 3 so the final answer is:

y = (1/9)(sqrt(x^2-25)^(3/2)) + 3

Please let me know if you need any clarification. I'm always happy to answer your questions.

Wbanguna U. (87)
UT Austin

Anonymous
Very useful material for studying!

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4