Look at your signs on the exponents before you intergrate and be careful, that should take care of it.cd246 said:Homework Statement
(x^2+3x-1)/x^4 the answer is,(-x^-1)-(3/2)(x^-2)+(1/3)(x^-3)+CHomework Equations
Just reverse diferentiationThe Attempt at a Solution
=x^2+3x-1+x^-4
=(x^3)/(3)+(3x^2)/(2)-x+(1/3)(x^-3+C)
(1/3)(x^3)+(3/2)(x^2)-x+(1/3)(x^-3)+C
I know i got the answer but somehow it is backwards(exponents mostly). What am I doing wrong?
cd246 said:Homework Statement
(x^2+3x-1)/x^4 the answer is,(-x^-1)-(3/2)(x^-2)+(1/3)(x^-3)+C
Homework Equations
Just reverse diferentiation
The Attempt at a Solution
=x^2+3x-1+x^-4
=(x^3)/(3)+(3x^2)/(2)-x+(1/3)(x^-3+C)
(1/3)(x^3)+(3/2)(x^2)-x+(1/3)(x^-3)+C
I know i got the answer but somehow it is backwards(exponents mostly). What am I doing wrong?
malawi_glenn said:Remember in "backwards differentiation":
i) Exponent +1
ii) divide with the new exponent.
[tex](x^2+3x-1)/x^4 = x^{-2} + 3x^{-3} - x^{-4} [/tex]
the first term:
[tex]x^{-2} \rightarrow (x^{-2+1})/(-2+1) = -x^{-1}[/tex]
etc.
Reverse differentiation problem is a mathematical concept that involves finding the original function when only the derivative of the function is known. It is also known as the inverse differentiation problem.
Reverse differentiation problem is important in many areas of science and engineering, such as physics, economics, and control theory. It allows us to determine the original function from its derivative, which is useful in understanding the behavior of systems and making predictions.
Reverse differentiation problem can be solved using different techniques, such as integration, inverse trigonometric functions, and logarithmic functions. It requires a good understanding of mathematical principles and techniques.
Reverse differentiation problem has many applications in real-world problems, such as in finding the original displacement or velocity from the acceleration of an object, determining the original function from its rate of change, and calculating the original demand or supply curve from the marginal cost or revenue.
Solving reverse differentiation problem can be challenging because there is no unique solution in many cases. It is also important to consider the domain and range of the original function and make sure that the solution is valid for all values of the independent variable.