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anonymous
 one year ago
Simple calculus question
anonymous
 one year ago
Simple calculus question

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nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0So simple it has no answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im stuck on a specific type of question, can someone help me?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2do you know the integration of sec(t) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Why is that necessary?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2its not really, but its a good check ...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im not quite sure where sec come into this.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2sec and csc have similar derivatives i recall sec and then adjust for csc

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2the integration of sec was well known prior to the founding of integration :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The derivative of csc i believe is cscxcotx

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2the derivative yes, but the integration? its a sneaky little trick

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{csc}{1}*\frac{csccot}{csccot}\] \[\frac{csc^2csc~cot}{csccot}\implies~ln(csc+cot)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im lost, simply how do you go from a derivative to an integral which is equal to the original function. Is it as simple as moving the derivative into the integral?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's the fundamental theorem of calculus \[\frac{ d }{ dx } \int\limits_{a}^{x} f(t) dt = f(x)\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2we have 2 options, we can use the fundamental thrm: \[\int_{a}^{x}f'(t)dt=F(x)F(a)\] and take the derivative \[\frac d{dx}\int_{a}^{x}f'(t)dt=f'(x)x'f'(a)a'\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the derivative of the integral of a function in that format is equal to that function.. so since i have the derivative do i find the antiderivative and plug that into the integral?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2or we can work the integration, and then take the derivative, either way

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0My course has recently worked with the fundamental therom so I assume thats the way they want me to solve it.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2you asked about which one it shouldbe, im just suggesting that in a pinch, you can work the long way if possible

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So... does that make the answer b or am i on the wrong route?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It seems to me this problem is designed to be simple im just making it difficult.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2it is designed to make you apply the fundamental thrm yes

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hey sorry, how did you get \[\frac{\csc^2\csc~\cot}{\csc\cot}\implies~\ln(\csc+\cot)\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2prolly an error in my head, thinkig to quick ln(csc + cot) derives to csc like i said, im used to the sec form :)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2x should be the high range, so its either the first or last option to me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the negation flips the limits, correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know its not c (duh). I dont believe it is a. However i dont know whether i put the antiderivtive of the derivitive into the intergral or the derivative into the integral

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2ln(csc(x)+cot(x)) + C derives to csc(x) since y = ln(csc(x)+cot(x)) + C, i dont see why we would have a constant in the integration when dy/dx = csc(x)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2a or d is my thought

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the constant i believe has something to do with making the y value correct, they all have them so i think its correct.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0A or D was what i started stuck between XD

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2\[y=\int y'(t)~dt +C\] i see it now, these old eyes were placing it inside the dt

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0XD thats a correct therom? so that would make it d?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Essentially there youre using the intergral to find the antiderivative?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2lets do the long way and check it out \[y=\int_{a}^{x}csc(t)~dt+C=ln(csc(x)+cot(x))+ln(csc(a)+cot(a))+C~\] when x=4, y=9 \[9+ln(csc(4)+cot(4))=ln(csc(a)+cot(a))+C\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2im using the integral to determine that solution yes :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks :) It really was simple XD

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2notice that by comparing like parts: ln(csc(4)+cot(4)) = ln(csc(a)+cot(a)) , let a=4 9 = C ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2another way to have viewed this, now that i have my bearings straight might be like this: 4 is in the domain element, it gets used as an input value ... it should be in the limit interval 9 is a range element, its not necessarily a part of the integrals domain limits

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2but thats just a guess at what i see, i would not have determined that by just the FTC

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks: i have actually solved this equation before (and whtat you are saying sounds farmilar) but i was dead tired and couldnnt remember how i did it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not to butt in, but why isn't the answer obviously 4?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Haha I was thinking the same thing, but anyway it was a nice question thanks @sccitestla and thanks @amistre64 :)
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