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anonymous
 5 years ago
cal 1 question
anonymous
 5 years ago
cal 1 question

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay so you can separate the integral like \[\int\limits_{5}^{1}f(x) dx= \int\limits_{5}^{0}82xdx+ \int\limits_{0}^{1}6x^2dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0technically you would have to evaluate the lower limit of the integral of the second term ( the 0 in the 6x^2 integral ) at some letter (a,b,c ect what ever letter you like). then you take the limit of the letter as it approaches the zero that is there as you see it above.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So in a more punctual approach the integral should be \[ \int\limits_{1}^{5}f(x) dx = \int\limits_{5}^{0}82x dx + \lim_{a \rightarrow 0} \int\limits_{a}^{1}6x^2dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's kind of technicality you will definitely see in later calculus called improper integrals. The REASON for this is because of the inequality \[x > 0\] which means the x on that interval never actually reaches zero, so you say as x > 0 (as x approaches zero, 0.00000001 and smaller). Now just take the integral of either one, the second one is the most correct if you understand the limit deal. but both will give you the same answer.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then how do u do it with that limit?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you would evaluate the integral first then take the limit. so \[\lim_{a \rightarrow 0} \int\limits_{a}^{1} 6x^2dx = \lim_{a \rightarrow 0} 6x^3/3 a \rightarrow1\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then \[6(1)^3/3  \lim_{a \rightarrow 0}6(a)^3/3 = 2(1)^3 \lim_{a \rightarrow 0}2(a)^3 = 2  0 = 2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But that's not the correct answer to it!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats only half of it though. you have to take the integral of the first half also, i was only showing how to do the limit part.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you see? so evaluate \[\int\limits_{5}^{0}82xdx\] and add two

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0answer should be 1027?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what is the answer? is it 1023?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can just type in the possible answers to see if thats right or wrong.. It doesn't tell the exact ans though
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