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1. If F(x) =  ∫ x^2 3  (sqrt(1+2t))/t dt, what is F'(x)?

2. If F(x) =  ∫ sinx  -112  sqrt(t)dt, what is F'(x)?

 Mar 25, 2019
 #1
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\(\dfrac{d}{dx} \displaystyle \int_{a(x)}^{b(x)}f(t)~dt = \\ f(b(x))\dfrac{db}{dx} - f(a(x))\dfrac{da}{dx}\)

 

\(\dfrac{d}{dx} \displaystyle \int_3^{x^2}\dfrac{\sqrt{1+2t}}{t}~dt = \\ \dfrac{\sqrt{1+2x^2}}{x^2}\cdot 2x - \dfrac{\sqrt{1+2(3)}}{3}\cdot 0 = \\ \dfrac{2\sqrt{1+2x^2}}{x}\)

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 Mar 25, 2019
 #2
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thank you so much! would there be any way i could start problem 2 out? :)

Guest Mar 25, 2019

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