- #1
phantomprime
- 7
- 0
Homework Statement
Homework Equations
n/a
The Attempt at a Solution
For the first one I tried to simplify it, though for some reason I don't think its the correct procedure.
If your teacher suggested partial fractions and you don't know what he's talking about, you have a serious problem. "Partial fractions" is a standard way to deal with problems like this and apparently your teacher has already taught you that (or tried to). Completely factor the denominator [x(x-1)(x+1)] and write the fraction as a sum of fractions each having one factor as denominator. If you don't know how to do "partial fractions", look it up in your textbook.phantomprime said:1: I simplified the dominator to x(x^2 -1)then i said U was equal to that. Now i don't know if i am starting off right..my professor was talking about something on "Integral of rational functions by partial fractions" and he said solve by that using the different cases. I really don't know what he's talking about. I looked in the book and that doesn't help much. I see the cases and all..but nothing similar to these problems.I looked online too and that's no help
Once again, there is a standard method for dealing with integrals of products of trig functions. In particular, there is a simple method for products of sine and cosine where one of them is to an odd power. Look it up in your textbook.2)I said a^2=16 and a is 4
i simplified it using integral notation to 1/4tan^-1 (x/4) to = ln|x+sqrt(x^2 + 4^2)|
3&4)... I really don't know where to begin
HOW did you convert it to that? The calculus book I have beside me gives, in a table of integrals,5. I converted that to ln |x+ sqrt(x^2 -1)|..but somehow I know my attempts are wrong
If your teacher suggested partial fractions and you don't know what he's talking about, you have a serious problem. "Partial fractions" is a standard way to deal with problems like this and apparently your teacher has already taught you that (or tried to). Completely factor the denominator [x(x-1)(x+1)] and write the fraction as a sum of fractions each having one factor as denominator. If you don't know how to do "partial fractions", look it up in your textbook.
If you are just looking to verify your answer, try http://integrals.wolfram.com/index.jsp. It won't help you solve the integrals though.phantomprime said:I know I have a serious problem in math, I don't need anyone to tell me that. Do you think I enjoy staying after class, asking people in class and even asking people online for help. I don't enjoy it, in fact I feel inferior becasue of it. I mean if one person can get it why can't I. I do it because it is required. So I can learn from it, I have done this with Physics as well and I mangaged to understand it. I have "Calculus of a Single variable" by james stuart. I look through it and yes it has partial fractions and all..but the thing is these problems are even numbered ones in the book. Even if I get an answer I don't know if its right or wrong. I wouldn't mind if there were odd so I can check them in the back.
phantomprime said:I know I have a serious problem in math, I don't need anyone to tell me that. Do you think I enjoy staying after class, asking people in class and even asking people online for help. I don't enjoy it, in fact I feel inferior becasue of it. I mean if one person can get it why can't I. I do it because it is required. So I can learn from it, I have done this with Physics as well and I mangaged to understand it. I have "Calculus of a Single variable" by james stuart. I look through it and yes it has partial fractions and all..but the thing is these problems are even numbered ones in the book. Even if I get an answer I don't know if its right or wrong. I wouldn't mind if there were odd so I can check them in the back.
Integration is a mathematical process used to find the area under a curve. It is important in science because it allows us to calculate quantities such as velocity, acceleration, and displacement, which are crucial in understanding the behavior of natural phenomena.
To solve integration problems, you need to follow a set of steps. First, identify the function that needs to be integrated. Then, use integration rules and techniques to simplify the function. Next, integrate the function using the identified rules and techniques. Finally, evaluate the integral to obtain the final answer.
Indefinite integration is the process of finding a general solution for a given function, while definite integration is used to find the exact value of an integral between two limits. Indefinite integration results in a constant of integration, while definite integration gives a specific numerical value.
Yes, integration can be used to solve real-world problems in a variety of fields such as physics, engineering, economics, and biology. It can be used to calculate areas, volumes, and other physical quantities that have real-world applications.
Integration is commonly used in science to calculate the work done by a force, the rate of change of a quantity, the center of mass of an object, the growth rate of a population, and the concentration of a substance in a solution. It is also used in fields such as signal processing, image processing, and data analysis.