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Jgeurts
 one year ago
Evaluate the following integrals. Show your work.
Jgeurts
 one year ago
Evaluate the following integrals. Show your work.

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zepp
 one year ago
Best ResponseYou've already chosen the best response.01/cos^2(x) is sec^2(x) and the integral of that is tan(x)

Jgeurts
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{2}x \sqrt{92x^2}dx\]

Jgeurts
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ d }{ dx }\int\limits_{x^2}^{sinx}\sqrt{1+t^2}dt\]

primeralph
 one year ago
Best ResponseYou've already chosen the best response.1no, just substitute, then everything falls out

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0use calculator so easy

Jgeurts
 one year ago
Best ResponseYou've already chosen the best response.0I need to do it without @best_mathematician

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2integral and derivative cancel each other out

Best_Mathematician
 one year ago
Best ResponseYou've already chosen the best response.0now u know wht to do right @Jgeurts

Jgeurts
 one year ago
Best ResponseYou've already chosen the best response.0@modphysnoob show me please

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{ d }{ dx }\int\limits_{x^2}^{sinx}\sqrt{1+t^2}dt\] after our supposed integration F(Sin(x))  F ( x^2) take dervaitve d/dx of F( Sin(x)) = cos(x) f(sin(x) d/dx of F(x^2) = f (x^2) 2x go back and plug into your funciton

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2f(t)= Sqrt[1+t^2] f(sin(x)= sqrt[1+ sin^2(x)] f(sin(x)*cos(x)= sqrt[1+ sin^2(x)]* cos(x)

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2now the bottom part f(x^2)2x=sqrt[1+x^2]2x

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2sqrt[1+ sin^2(x)]* cos(x)sqrt[1+x^2]2x

Jgeurts
 one year ago
Best ResponseYou've already chosen the best response.0Im formulating my question, haha

Jgeurts
 one year ago
Best ResponseYou've already chosen the best response.0so the d/dx means derive the interval?

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2yes, since we are taking a function integrate it and derive , it undoes the integration

Jgeurts
 one year ago
Best ResponseYou've already chosen the best response.0haha great! i get it, thank you, that one was super hard!

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2I can show you an easy example if you like?

Jgeurts
 one year ago
Best ResponseYou've already chosen the best response.0@modphysnoob sure that would be great, im learning for my final :)

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2let's to a problem like yours but with easier integrand dw:1367723123193:dw

Jgeurts
 one year ago
Best ResponseYou've already chosen the best response.0so we would derive sinx to cosx and x2 to 2x

Jgeurts
 one year ago
Best ResponseYou've already chosen the best response.0then plug in for t and subtract them from each other right?

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2so in this case f(t)= t when we integrate we will get a function which we will call F(t) F(t) is evaluated at F(sin(x))  F( x^2) then taken d/dx of d/dx( F(sin(x))  F( x^2) ) using chain rule d/dx ( F(sin(x)) = cos(x) f( sin(x)

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2which is cos(x) sin(x)

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2let's do botttom part d/dx( F (x^2) = 2x f( x^2) 2x x^2= 2x^3

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2so cos(x) sin(x)2x^3

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.2this is easy integrand so we could actually integrate it and then differntiate it to confirm out result. Integrate t t^2/2 plug in limits (sin^2 x)/2  x^4/2 take derivative d/dx cos(x) sin(x) 2x^3

Jgeurts
 one year ago
Best ResponseYou've already chosen the best response.0Yes thats great! thank you so much! @modphysnoob
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