What is #f(x) = int sqrt(x+8) dx# if #f(2)=-3 #?
I got:
Have a look:
By signing up, you agree to our Terms of Service and Privacy Policy
To find ( f(x) = \int \sqrt{x+8} , dx ) given that ( f(2) = -3 ), you need to find the antiderivative of ( \sqrt{x+8} ), then evaluate it at ( x = 2 ) and use the given value to solve for the constant of integration.
First, find the antiderivative of ( \sqrt{x+8} ):
[ \int \sqrt{x+8} , dx = \frac{2}{3} (x + 8)^{3/2} + C ]
Given that ( f(2) = -3 ), substitute ( x = 2 ) into the antiderivative:
[ -3 = \frac{2}{3} (2 + 8)^{3/2} + C ]
[ -3 = \frac{2}{3} (10)^{3/2} + C ]
[ -3 = \frac{2}{3} \times 10 \times \sqrt{10} + C ]
[ -3 = \frac{20}{3} \sqrt{10} + C ]
[ C = -3 - \frac{20}{3} \sqrt{10} ]
Now, substitute the value of ( C ) back into the antiderivative:
[ f(x) = \frac{2}{3} (x + 8)^{3/2} - 3 - \frac{20}{3} \sqrt{10} ]
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.
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.
- How do you integrate #int (x+5)^6# using substitution?
- How do you integrate #int (x^5 + 1)/(x^6 - x^4)# using partial fractions?
- How do you find the integral of #1/sqrt(x^2 -4)#?
- How do you integrate #int ((x-3)(x-1))/(-x(x-5)) dx# using partial fractions?
- How do you find the antiderivative of #int sin^3xcosxdx#?

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