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  • hba

Can anyone help me i almost forgot what integration is ?

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What kind of integration (what functions)?
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...
  • hba
\[1)\int\limits_{}^{}sinf(x).f'(x)dx=-cosf(x)+c\] \[2)\int\ Cosf(x).f'(x)dx=Sinf(x)+c\] \[3)\int\limits_{}^{}\tan f(x).f'(x)dx=lnsecf(x)+c\] \[4)\int\ Secf(x).f'(x)dx=\ln \left[ secf(x)+tanf(x) \right]\] \[5)\int\limits_{}^{}Cotf(x).f'(x)dx=lnsinx+c\] \[6)\int\limits_{}^{} Cosec f(x).f'(x)dx=\ln(cosecf(x)-cotf(x) ) +c\] \[7)\int\ Sec^2f(x).f'(x)dx=tanf(x)+c\] \[8)\int\limits_{}^{}Cosec^2f(x).f'(x)dx=-Cot f(x)+c\] \[9)\int\limits_{}^{}Sec f(x).Cosecf(x).f'(x)dx=Secf(x)\] I do remember some of these .

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Other answers:

u want more formulas?
  • hba
Yeah thanks.
  • hba
@hartnn What about the tricks ? I think i forgot them When we have a cycle from 0 to pi i guess.
yeah... from 0 to 2pi, integration of sin and cos is 0....
do u want it properly in latex from, or in words form ??
  • hba
@hartnn Latex form with some examples please.
have patience, it will take time...
  • hba
Yeah lol thanks i am waiting :)
\(\color {red} {\text{ If m,n are Integers } \\ \text{Set I : } \\\int \limits_0^{2 \pi} \sin nx = 0 \\\int \limits_0^{2 \pi} \cos nx = 0 \\\int \limits_0^{2 \pi} \sin nx . \cos nx = 0 \\ \int \limits_0^{2 \pi} \sin nx \sin mx = 0 [m \ne n] \\\int \limits_0^{2 \pi} \cos nx \cos mx = 0 [m \ne n]}\)
\(\color{red}{\text{Set II :}\\ \int \limits_0^{2 \pi}\sin^2nx =\pi \\\int \limits_0^{2 \pi}\cos^2nx =\pi }\)
sorry i am missing dx everywhere
\(\color {red}{\\\int \limits_0^{\color{blue }{n}\pi}\sin^2nx=\color{blue}{n}\pi/2 \\ }\) \(\color {red}{\\\int \limits_0^{\color{blue }{n}\pi}\cos^2nx=\color{blue}{n}\pi/2 \\ }\)
\(\color{red}{\int \limits_0^\pi\sin mx.\sin nx=0(m \ne n)}\) \(\color{red}{\int \limits_0^\pi\cos mx.\cos nx=0(m \ne n)}\)
thats all i have...
  • hba
Yaar @hartnn Is mai koi odd or even ka scene bhi hota hai na ?
generally, if the function f(x) is odd, then \(\huge \int \limits_{-a}^af(x)=0 \) if the function f(x) is even \(\huge \int \limits_{-a}^af(x)=2\int \limits_{0}^af(x) \)
  • hba
@hartnn Set hai,Thanks a lot :)
  • hba
@hartnn Acha aik example show krdo mujhe ?
example for which formula ?
  • hba
Jo odd or even hai na uss kai liyee.
u know how to find even / odd function ?
\(\huge \int \limits_{-a}^a(x^3-x) dx=... \\ \huge \int \limits_{-\pi/2}^{\pi/2}\sin^3x dx=...\)
  • hba
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.
\(\huge \int \limits_{-\pi}^{\pi}\sin2x.\sin5x dx=.... \\\huge \int \limits_{-a}^ax^4+x^2+1.dx=....\)
sin (-x) = -sin x <----odd cos(-x) = cos x <----even
  • hba
Oh sahi hai :)
  • hba
Acha or hyperbolic function ka kia hota hai integration mai ?
mere link me hai, hyperbolics....
  • hba
Chalo let me check
  • hba
thanks a lot :)
got it ? for properties of definite integrals 12th one is my fav....
challenge Q, if any1's interested ..... PROVE \(\int\limits_{0}^{\pi} \ln \sin(x)=-\pi \ln(2)\) i've solved that on OS...

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