You are here:
Calculus/Calculus
Advertisement
Question
1.I am integrating sqrt(x^2+a^2) by parts,but I came to the point when I have find the derivative of sqrt(x^2+a^2),and I don't know what to do and which formula to use pls help me.
2.I have to find the integral of (2x+a)/sqrt(x^2+ax),i just don't know which formula to use as I am in earlier stage of calculating the integral of sqrt(a+x)/sqrtx and it is the part of this question.
3.I also want to find the derivative of asin^2(x)+bcos^2(x)
1. The problem needs to be integrated by a trig substitution.
Draw a right triangle with the far side x from the angle Θ and the near side a to the angle Θ. Then tan(Θ)=x/a, or a*tan(Θ)=x. The integral becomes a√(tan˛Θ+1) = a*sec(Θ) with the dx being asec˛(x). In the end, you have the integral of a˛sec^3(Θ) dΘ.
Note that sec˛(Θ) = 1 + tan˛(Θ), so the problem is to integrate
a˛sec(Θ)(1+tan˛(Θ)). Multiply this out and both expression can be integrated with basic trig identities of integration.
2. Let u=x˛+ax, then du=2x+a. Do a u substitution in this way.
3. The derivative of any function squared, f˛(x), is 2f(x)f'(x). This can be applied to sin˛(x) and cos˛(x). Once this has been done, both terms will both involve a sin(x)cos(x) and can be combined.
Related Articles
Answers by Expert:
Scotto
Expertise
Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.
Experience
Experience in the area: I have tutored students in all areas of mathematics for over 25 years.
Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors.
Awards and Honors: I have passed Actuarial tests 100, 110, and 135.
Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC.
Well over 2,000 of them have been in calculus.
Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required.
I graduated with honors in both my BS and MS degree from Oregon State University.
I was allowed to jump into a few junior level courses my sophomore year.
Awards and Honors
I have been nominated as the expert of the month several times.
All of my scores right now are at least a 9.8 average (out of 10).
Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.
©2012 About.com, a part of The New York Times Company. All rights reserved.