# Thread: The Fundamental Theorem of Calculus

1. ## The Fundamental Theorem of Calculus

4 integral 9 2xsquare root 2

2. Is this it: $\int_4^9 2 \sqrt{2} \ dx$

Factor out the constant: $2\sqrt{2} \int_4^9 dx$

Use the fact that: $\int x^{n}\ dx = \frac{x^{n+1}}{n} + C$

Here imagine $n = 0$ : $\int_4^9 x^0 \ dx$

3. I'm sorry inside the square root is x

4. Like this? $\int_4^92\sqrt{2x} \ dx$

Remember that square roots can be written as exponent (1/2). So factor out the constant to get: $2\int_4^9 (2x)^{\frac{1}{2}} \ dx$

Use the sub: $u = 2x \ \Rightarrow \ du = 2 dx \ \Leftrightarrow \ \frac{du}{2} = dx$