AboutScotto Expertise Any kind of mathematics (algebra, geometry, trigonometry, matrices, calculus, linear approximation, linear regression, linear programming, numerical analysis, probability, statistics, etc.). I also have answered some questions in Physics, Chemistry, and Biology. I would like to volunteer in all areas of Mathematics, not just calculus, and the other three courses that were mentioned.
Experience Experience in the area: I have tutored students in all areas of mathematics for over 20 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.
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)
Answer 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.
