Integration: Solve x^2-3x+2 Over x+1

In summary, when faced with the problem of integrating (x^2-3x+2)/(x+1)dx, it is recommended to divide the polynomial into three separate integrals. Alternatively, one can use long division to simplify the expression before integrating.
  • #1
kingdomof
105
0

Homework Statement



Int(x^2-3x+2)/(x+1)dx



Homework Equations





The Attempt at a Solution



I don't know where to start.
 
Physics news on Phys.org
  • #2
Start by dividing the two polynomials. The resultant expression will be much simpler.
 
  • #3
kingdomof said:

Homework Statement



Int(x^2-3x+2)/(x+1)dx



Homework Equations





The Attempt at a Solution



I don't know where to start.

Instead of trying to factor simply divide it into 3 different equations i.e.


[tex]\int \frac{x^{2}}{x+1}dx - \int \frac{3x}{x+1}dx + \int \frac{2}{x+1}dx[/tex]
 
  • #4
djeitnstine said:
Instead of trying to factor simply divide it into 3 different equations i.e.


[tex]\int \frac{x^{2}}{x+1}dx - \int \frac{3x}{x+1}dx + \int \frac{2}{x+1}dx[/tex]
These aren't equations: they are expressions.

A much simpler approach is to do as jgens advised, and divide x^2 - 3x + 2 by x + 1, using long division.
 

1. What is integration?

Integration is a mathematical process that involves finding the area under a curve. It is the inverse operation of differentiation, and it allows us to find the original function when we know its derivative.

2. How do you solve an integration problem?

To solve an integration problem, we first need to identify the function that we want to integrate. Then, we use integration techniques, such as substitution, integration by parts, or partial fractions, to find the antiderivative of the function. Finally, we evaluate the antiderivative at the given limits to find the definite integral.

3. What is the given integration problem: x^2-3x+2 over x+1?

The given integration problem is asking us to find the integral of the function f(x) = x^2-3x+2 over the interval [x, x+1]. In other words, we need to find the area under the curve of the given function between the limits of x and x+1.

4. What is the general formula for solving integration problems?

The general formula for solving integration problems is given by the Fundamental Theorem of Calculus, which states that the definite integral of a function f(x) can be found by evaluating its antiderivative F(x) at the upper and lower limits of integration, represented by a and b, and then taking the difference between the two values. In other words, ∫(f(x)) dx = F(b) - F(a).

5. How do you solve the given integration problem: x^2-3x+2 over x+1?

To solve the given integration problem, we first use the formula for the integral of a polynomial function to find the antiderivative of f(x) = x^2-3x+2, which is F(x) = 1/3x^3 - 3/2x^2 + 2x. Then, we evaluate F(x) at the limits of x and x+1 to get the definite integral. The final answer is 1/3(x+1)^3 - 3/2(x+1)^2 + 2(x+1) - (1/3x^3 - 3/2x^2 + 2x).

Similar threads

  • Calculus and Beyond Homework Help
Replies
10
Views
282
  • Calculus and Beyond Homework Help
2
Replies
44
Views
3K
  • Calculus and Beyond Homework Help
Replies
4
Views
770
  • Calculus and Beyond Homework Help
Replies
7
Views
640
  • Calculus and Beyond Homework Help
Replies
5
Views
919
  • Calculus and Beyond Homework Help
2
Replies
54
Views
7K
  • Calculus and Beyond Homework Help
Replies
3
Views
268
  • Calculus and Beyond Homework Help
Replies
6
Views
505
  • Calculus and Beyond Homework Help
Replies
2
Views
276
  • Calculus and Beyond Homework Help
Replies
3
Views
768
Back
Top