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agent0smithBest ResponseYou've already chosen the best response.0
What kind of integration (what functions)?
 one year ago

agent0smithBest ResponseYou've already chosen the best response.0
For definite integrals, the purpose is to find area under a curve. Indefinite integrals are handy for finding a function, given the rate of change of that function. idk if this is what you want...
 one year ago

hbaBest ResponseYou've already chosen the best response.0
\[1)\int\limits_{}^{}sinf(x).f'(x)dx=cosf(x)+c\] \[2)\int\ Cosf(x).f'(x)dx=Sinf(x)+c\] \[3)\int\limits_{}^{}\tan f(x).f'(x)dx=lnsecf(x)+c\] \[4)\int\ Secf(x).f'(x)dx=\ln \left[ secf(x)+tanf(x) \right]\] \[5)\int\limits_{}^{}Cotf(x).f'(x)dx=lnsinx+c\] \[6)\int\limits_{}^{} Cosec f(x).f'(x)dx=\ln(cosecf(x)cotf(x) ) +c\] \[7)\int\ Sec^2f(x).f'(x)dx=tanf(x)+c\] \[8)\int\limits_{}^{}Cosec^2f(x).f'(x)dx=Cot f(x)+c\] \[9)\int\limits_{}^{}Sec f(x).Cosecf(x).f'(x)dx=Secf(x)\] I do remember some of these .
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
http://openstudy.com/users/hartnn#/updates/50960518e4b0d0275a3ccfba
 one year ago

hbaBest ResponseYou've already chosen the best response.0
@hartnn What about the tricks ? I think i forgot them When we have a cycle from 0 to pi i guess.
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
yeah... from 0 to 2pi, integration of sin and cos is 0....
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
do u want it properly in latex from, or in words form ??
 one year ago

hbaBest ResponseYou've already chosen the best response.0
@hartnn Latex form with some examples please.
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
have patience, it will take time...
 one year ago

hbaBest ResponseYou've already chosen the best response.0
Yeah lol thanks i am waiting :)
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
\(\color {red} {\text{ If m,n are Integers } \\ \text{Set I : } \\\int \limits_0^{2 \pi} \sin nx = 0 \\\int \limits_0^{2 \pi} \cos nx = 0 \\\int \limits_0^{2 \pi} \sin nx . \cos nx = 0 \\ \int \limits_0^{2 \pi} \sin nx \sin mx = 0 [m \ne n] \\\int \limits_0^{2 \pi} \cos nx \cos mx = 0 [m \ne n]}\)
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
\(\color{red}{\text{Set II :}\\ \int \limits_0^{2 \pi}\sin^2nx =\pi \\\int \limits_0^{2 \pi}\cos^2nx =\pi }\)
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
sorry i am missing dx everywhere
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
\(\color {red}{\\\int \limits_0^{\color{blue }{n}\pi}\sin^2nx=\color{blue}{n}\pi/2 \\ }\) \(\color {red}{\\\int \limits_0^{\color{blue }{n}\pi}\cos^2nx=\color{blue}{n}\pi/2 \\ }\)
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
\(\color{red}{\int \limits_0^\pi\sin mx.\sin nx=0(m \ne n)}\) \(\color{red}{\int \limits_0^\pi\cos mx.\cos nx=0(m \ne n)}\)
 one year ago

hbaBest ResponseYou've already chosen the best response.0
Yaar @hartnn Is mai koi odd or even ka scene bhi hota hai na ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
generally, if the function f(x) is odd, then \(\huge \int \limits_{a}^af(x)=0 \) if the function f(x) is even \(\huge \int \limits_{a}^af(x)=2\int \limits_{0}^af(x) \)
 one year ago

hbaBest ResponseYou've already chosen the best response.0
@hartnn Set hai,Thanks a lot :)
 one year ago

hbaBest ResponseYou've already chosen the best response.0
@hartnn Acha aik example show krdo mujhe ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
example for which formula ?
 one year ago

hbaBest ResponseYou've already chosen the best response.0
Jo odd or even hai na uss kai liyee.
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
u know how to find even / odd function ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
\(\huge \int \limits_{a}^a(x^3x) dx=... \\ \huge \int \limits_{\pi/2}^{\pi/2}\sin^3x dx=...\)
 one year ago

hbaBest ResponseYou've already chosen the best response.0
Mujhe pata hai even/odd function kia hota hai trignometric mai sahi sai yaad nahi shayad sin and cos hota hai even or baki odd.
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
\(\huge \int \limits_{\pi}^{\pi}\sin2x.\sin5x dx=.... \\\huge \int \limits_{a}^ax^4+x^2+1.dx=....\)
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
sin (x) = sin x <odd cos(x) = cos x <even
 one year ago

hbaBest ResponseYou've already chosen the best response.0
Acha or hyperbolic function ka kia hota hai integration mai ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
mere link me hai, hyperbolics....
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
got it ? for properties of definite integrals http://www.pinkmonkey.com/studyguides/subjects/calc/chap7/c0707501.asp 12th one is my fav....
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
challenge Q, if any1's interested ..... PROVE \(\int\limits_{0}^{\pi} \ln \sin(x)=\pi \ln(2)\) i've solved that on OS...
 one year ago
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