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roselin
 2 years ago
definite integral from pi/2 to 0 (2+tan1/2)sec^2 t/2 dt
roselin
 2 years ago
definite integral from pi/2 to 0 (2+tan1/2)sec^2 t/2 dt

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roselin
 2 years ago
Best ResponseYou've already chosen the best response.0sorry, it is actually tan t/2

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.2ok, use by integral substitution u = tan 1/2 t du = .... ?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.2opss.. u = 2+tan1/2 t, i meant :)

roselin
 2 years ago
Best ResponseYou've already chosen the best response.0where did you take the half from?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.2u = 2 + tan1/2 t du = 0 + 1/2 sec^2 1/2 t dt right ?

roselin
 2 years ago
Best ResponseYou've already chosen the best response.0definite integral from pi/2 to 0 (2+tan t/2)sec^2 t/2 dt

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.0When deciding what to make your substitution with, you should consider what in the integral has its derivative in there too. This sort of is the process of reversing the chain rule. In this case you should remember that the derivative of tangent is secant squared.

roselin
 2 years ago
Best ResponseYou've already chosen the best response.0so where did u get that 1/2 from? I did not get it, sorry

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ t }{ 2 }=\frac{ 1 }{ 2 }t\]

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.0In the same way 4/2 is equal to 4*(1/2)

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.2by using the chain rule : if y=tanAx then y'=A*sec^2 Ax

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.2so, the integration will be int 2u du right ?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.2ok, what's the result it ...?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.2int (2u du) = u^2 right ?

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.0Assuming this is right, you need to remember that the problem you were given to solve had no "u" in it at all, so you must plug in "u" back to the equation to get it in terms of "x".

roselin
 2 years ago
Best ResponseYou've already chosen the best response.0so is that ( tan 1/2 t)^2 ?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.2(2 + tan 1/2 t)^2 now, plug and calculate for t = 0 and t =pi/2

roselin
 2 years ago
Best ResponseYou've already chosen the best response.0tan of 0= 0 and tan of pi/4 = 1

tanjung
 2 years ago
Best ResponseYou've already chosen the best response.0(2 + tan 1/2 (0))^2  (2 + tan 1/2 (pi/2))^2 = (2+tan(0))^2  (2+tan(pi/4)^2 = (2+0)^2  (2  tan(pi/4))^2 = 4  (2  1)^2 = 4  1 = 3 if i dont make mistake :)

roselin
 2 years ago
Best ResponseYou've already chosen the best response.0and where do i put te integral sign ?

tanjung
 2 years ago
Best ResponseYou've already chosen the best response.0just remember that int (f(x)) dx [a,b] = [F(x)] [a,b] = F(b)F(a) after u integrate it, u got (2 + tan 1/2 t)^2 right ? now, substitute for highest interval (t=0) and then subtract with for t=pi/4 (low interval)

tanjung
 2 years ago
Best ResponseYou've already chosen the best response.0do u have the options ?

roselin
 2 years ago
Best ResponseYou've already chosen the best response.0no, but i used the wolfram and shows the ans is 5

roselin
 2 years ago
Best ResponseYou've already chosen the best response.0i have another question, how would I put this problem in wolframaalpha? dw:1355919813662:dw

tanjung
 2 years ago
Best ResponseYou've already chosen the best response.0sorry, i cant do it in wolfram :)
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