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Math Help - The Fundamental Theorem of Calculus

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    The Fundamental Theorem of Calculus

    4 integral 9 2xsquare root 2
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  2. #2
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    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
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    I'm sorry inside the square root is x
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    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
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