∫(x^3-x^2)/x^2
I got (x^2)/(2)-x + C but that's not one of the answers
Options
x - 1 + C
(x^2/2)-(x^3/3) + C
(x^4-x^3)/4x^2 + C
(x^2/2) -x + C
∫(x^3-x^2) dx/x^2 =∫(x^3/x^2-x^2/x^2)dx
= ∫(x^3/x^2-x^2/x^2)dx
= ∫(x-1)dx
= (x^2/2) - x + c
which is the fourth option and is also what you got
Oh shoot I misread my answer. Thanks
You are welcome.
To find the antiderivative of the given function ∫(x^3-x^2)/x^2, we can divide the two terms separately.
First, let's divide x^3/x^2:
x^3/x^2 = x^(3-2) = x^1 = x
Next, let's divide -x^2/x^2:
-x^2/x^2 = -x^(2-2) = -x^0 = -1
Now, we can rewrite the integral as ∫(x - 1) dx.
To integrate ∫(x - 1) dx, we can apply the power rule of integration, which states that integrating x^n gives (x^(n+1))/(n+1).
Applying this rule to both terms, we get:
∫(x - 1) dx = (x^2)/2 - x
Therefore, the correct answer is (x^2/2) - x + C.
However, you mentioned that this is not one of the given options. Let's check the options provided:
Option 1: x - 1 + C
This does not match the solution.
Option 2: (x^2/2) - (x^3/3) + C
This does not match the solution either.
Option 3: (x^4 - x^3)/(4x^2) + C
This option is incorrect as it involves a division by x^2, which is not present in the original function.
Option 4: (x^2/2) - x + C
This matches the correct solution we found earlier.
Therefore, the correct answer is (x^2/2) - x + C.