# Solve for y: F(3) = 1/4; Integration: f(3) = 1/4; y = 1/(6x-x^2+13)

• UrbanXrisis
In summary, after solving the given equation f(3)=1/4, \int\frac{dy}{y}=\int (6-2x)dx, and substituting the values, the correct answer is y=\frac{1}{6x-x^2+13}. However, there seems to be confusion about the value of C, with some sources stating it is 13 and others stating it is -13. Further clarification is needed to determine the correct value of C.
UrbanXrisis
f(3)=1/4

$$\int\frac{dy}{y}=\int (6-2x)dx$$
$$-\frac{1}{y}=6x-x^2+C$$
$$-4=18-9+C$$
$$C=-13$$
$$-\frac{1}{y}=6x-x^2-13$$
$$y=-\frac{1}{6x-x^2-13}$$
$$y=\frac{1}{6x-x^2+13}$$

why?

Looks like the answer is wrong.

I think that the negative was distributed before the Constant was added.. I just don't know why?

$$\int \frac{dy}{y}$$ is not $$\frac{-1}{y}$$

sorry, it's y^2

f(3)=1/4

$$\int\frac{dy}{y^2}=\int (6-2x)dx$$
$$-\frac{1}{y}=6x-x^2+C$$
$$-4=18-9+C$$
$$C=-13$$
$$-\frac{1}{y}=6x-x^2-13$$
$$y=-\frac{1}{6x-x^2-13}$$
$$y=\frac{1}{6x-x^2+13}$$

why?

$$-\frac{1}{y}=6x-x^2+C$$

$$y = -\frac{1}{6x-x^2+c}$$

$$-\frac{1}{4} = \frac{1}{9+C}$$

C = 13

sub that back in... you get the same equation as I do...

I'm sorry, C is -13, and yeah, the one you got is correct.

I don't see how they got that answer...

Last edited by a moderator:
You wrote the answer in correct in your first post, and unless there's a new math system where

C + 9 = 4, and C = 18 theyre wrong. C is -13

I took the answers right off of the college-board website! wow...

Nobody's infall-yable.

## 1. What is the value of y when F(3) = 1/4?

The value of y when F(3) = 1/4 is 1/(6x-x^2+13).

## 2. How is integration used to solve for y in this equation?

Integration is used to find the antiderivative of the given function f(x). Once the antiderivative is found, the value of y can be determined by substituting the given value of x = 3 into the antiderivative.

## 3. What is the significance of the value of y in this equation?

The value of y represents the vertical position on the graph of the function f(x) at the given value of x = 3. It is a solution to the equation F(3) = 1/4, which means that it satisfies the given conditions.

## 4. Can this equation be solved for other values of x?

Yes, this equation can be solved for any value of x, as long as the denominator 6x-x^2+13 does not equal 0. This is because division by 0 is undefined.

## 5. What are the steps to solve for y in this equation?

The steps to solve for y in this equation are:

1. Find the antiderivative of the function f(x).
2. Substitute the given value of x = 3 into the antiderivative to find the value of y.

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