- #1
kingdomof
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Homework Statement
Int(x^2-3x+2)/(x+1)dx
Homework Equations
The Attempt at a Solution
I don't know where to start.
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.
These aren't equations: they are expressions.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]
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.
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.
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.
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).
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).