# What is #f(x) = int xsqrt(5-2) dx# if #f(2) = 3 #?

The function

First, compute the integral:

Power rule:

If you would like, you can rewrite it as:

Hope this helped!

By signing up, you agree to our Terms of Service and Privacy Policy

To find ( f(x) = \int x \sqrt{5 - 2x} , dx ) when ( f(2) = 3 ), we need to find the definite integral of the given function and then use the given value to determine the constant of integration.

Since ( f(2) = 3 ), this means:

[ \int_{2}^{2} x \sqrt{5 - 2x} , dx = 3 ]

This integral evaluates to zero since the lower and upper limits of integration are the same.

Now, we have:

[ \int_{2}^{x} x \sqrt{5 - 2x} , dx = f(x) - f(2) ]

We need to evaluate this integral to find ( f(x) ). Then we can use the given information to find the value of ( f(x) ).

After evaluating the integral, we find:

[ f(x) = \frac{5}{12} (5 - 2x)^{3/2} + C ]

Now, we use the given value ( f(2) = 3 ) to find the constant of integration ( C ).

[ 3 = \frac{5}{12} (5 - 2(2))^{3/2} + C ]

[ 3 = \frac{5}{12} (5 - 4)^{3/2} + C ]

[ 3 = \frac{5}{12} (1)^{3/2} + C ]

[ 3 = \frac{5}{12} + C ]

[ C = 3 - \frac{5}{12} ]

[ C = \frac{31}{12} ]

Therefore, the function ( f(x) ) is:

[ f(x) = \frac{5}{12} (5 - 2x)^{3/2} + \frac{31}{12} ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7