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anonymous
 5 years ago
Differentiate: 1/(2x1)^(1/2) dx from x=5 to x=13
anonymous
 5 years ago
Differentiate: 1/(2x1)^(1/2) dx from x=5 to x=13

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Use a u sub, and then F(13)F(5)

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1if you can differentiate \[\int\limits 1/x dx\] then you will know how to do it. do you need more help ?

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1your integral looks awfully like 1/x, it's just shifted a little. you you can guess that it is the family of 1/x. can you integrate 1/x ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That's what I meant, lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I just really don't understand definite integrals.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1now your goal is to make the integral look like that by letting u = 2x+1

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1oops, never mind about lnx, i did not see the ^1/2 part. so it will be a family of \[\int\limits 1/\sqrt(x)\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1after letting u = 2x1, \[\int\limits 1/\sqrt(u) dx\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1is what you are going to get, but the problem is that the integrand is now a function of u, which cannot be integrated over x. so you have to over come that by figuring out what "dx" is. that technique is the socalled usubstitution. do you know how to find dx ?

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1okay, so u = 2x1 right ? if you differentiate both sides with respect to x, d/dx(u) = d/dx(2x1) d/dx(u) = 2 do you get this so far ?

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1so if you multiply dx on both sides and divide 2 on both sides, you will get 1/2 du = dx this is what is happening, but it is traditional and easier to say u=2x1 du = 2 dx by differentiating both sides

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1so once you substitute dx with the above equation, your integral becomes\[1/2\int\limits 1/\sqrt(u) du\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1now it is important to know that the limits of the integration will change as well, unless you want to know how to do that I won't go into the detail. to avoid having to change the limits, you will find out the indefinite integral first, then substitute 2x1 back into u. that way you can plug in the limits again.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1\[1/2\int\limits 1/\sqrt(u) du = 1/2 *1/2*(u^{1/2})+C\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.11/4(2x1) + C =F(x) so F(13) F(5) is your answer. just as a reminder, C will not matter so you can ignore it

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1woops\[1/4 \sqrt(2x1) +C\] is what I meant

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1it seems like the answer will be 3/4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, ok, I see. Thanks!!! Can you help me with a couple word problems too?

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1I need to go soon, so I can help you with one of them. ask me the one that you think need most help

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0A manufacturer has been selling flashlights at $6 a piece, and at this price consumers have been buying 3000 flashlights per month. The manufacturer wishes to raise the price and estimates that for each $1 increase in price, 1000 fewer flashlights will be sold each month. The manufacturer can produce the flashlight a cost of $4 per flashlight. At what price should the manufacturer sell the flashlights to generate the greatest profit?

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.1okay so what do you not get from this problem ?
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