Looks like a natural for trig substitutions for both integralsFuturEngineer said:Homework Statement
Evaluate
Integrate (2-3x/(Sqrt.(1 - x^2))) dx
Homework Equations
1/Sqrt.(1-x^2) = arctan
The Attempt at a Solution
I am so lost, but this is what I've tried, but didn't work...
I separated the integral into two so
Integral of (2/(Sqrt.(1-x^20))) dx - integral of (3x/(Sqrt.(1-x^2))) dx
I am not sure how to proceed? Help! [/B]
A trig substitution would work, but I agree that an ordinary substitution (as you suggest) would be easier, which makes it a better choice.HallsofIvy said:I would NOT use a trig substitution for [itex]\frac{3x}{\sqrt{1- x^2}}[/itex]. Instead let [itex]u= 1- x^2[/itex]
Splitting fractions (integrals) is a mathematical process used to simplify and solve complex fractions or integrals into smaller, more manageable parts. It involves breaking down the larger fraction or integral into smaller fractions or integrals that are easier to calculate.
Splitting fractions (integrals) can make solving complex mathematical problems easier and more efficient. It allows for a step-by-step approach to solving a problem, which can help in understanding the process and reaching the correct solution. It also helps to eliminate fractions or integrals that are difficult to calculate.
The first step is to factor the numerator and denominator of the fraction or integrand. Then, look for any common factors that can be canceled out. Next, split the fraction or integral into smaller parts by separating the numerator and denominator into their respective factors. Finally, simplify the resulting fractions or integrals and combine them to get the final solution.
Yes, Splitting fractions (integrals) can be used for both proper and improper fractions. However, the process may differ slightly for each type of fraction. For proper fractions, the resulting fractions may be simpler, while for improper fractions, the process may involve polynomial long division to simplify the resulting fractions.
While Splitting fractions (integrals) can be a useful tool in solving complex mathematical problems, it may not always be the most efficient method. In some cases, it may be easier to solve the fraction or integral using other techniques such as substitution or partial fractions. Additionally, Splitting fractions (integrals) may not always result in a simplified solution, and some fractions or integrals may still require further simplification.