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fortheloveofscience
 3 years ago
integrate the following
fortheloveofscience
 3 years ago
integrate the following

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fortheloveofscience
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{\Pi/2} \sin ^{2}x \div (\sin ^{2}x+4\cos ^{2}x)\]

perl
 3 years ago
Best ResponseYou've already chosen the best response.1so you have for the denominator sin^2 + 4(1sin^2) = sin^2 + 4  4 sin^2 3sin^2 + 4

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.0I think this is aprtial fractions. If you take cos^2 x common from denominator you have tan^2 x/(tan^2 x+4) Put tan x=t. you'll get dx=dt/sec^2 x= dt/(1+t^2). So you have t^2/((t^2+4)(t^2+1)). Do you know partial fractions?

perl
 3 years ago
Best ResponseYou've already chosen the best response.1you dont need partional fractions

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.0How will you do it by converting denominator to sin?

perl
 3 years ago
Best ResponseYou've already chosen the best response.1the denominator is 3sin^2 t + 4 , do long division

fortheloveofscience
 3 years ago
Best ResponseYou've already chosen the best response.0we gottta use the properties of definite integrals

perl
 3 years ago
Best ResponseYou've already chosen the best response.1shank, change cos^2 = 1  sin^2

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.0You're effectively doing the same thing only.

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.0By doing by partial fractions it reduces to the same thing. Only it is in terms of t^2 so easier to integrate. You directly get tan inverse form which is easy.

perl
 3 years ago
Best ResponseYou've already chosen the best response.1ok you did trig substitution

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.0For the second term you divide by cos ^2 and then you get tan form and then you put that as t to integrate, You get that directly by partial fractions in terms of t.

perl
 3 years ago
Best ResponseYou've already chosen the best response.1i see that, im asking about your t = tan x part

perl
 3 years ago
Best ResponseYou've already chosen the best response.1what sort of substitution is this called?

shankvee\
 3 years ago
Best ResponseYou've already chosen the best response.0Yeah thats a trignometric substituion.

perl
 3 years ago
Best ResponseYou've already chosen the best response.1ok your solution is better, im not sure if i would go ahead with mine . not sure what do do next

perl
 3 years ago
Best ResponseYou've already chosen the best response.1you can divide top and bottom by cos^2 for my solution

perl
 3 years ago
Best ResponseYou've already chosen the best response.1shank, can i ask a simple question about kites
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