Question

Can anyone help me i almost forgot what integration is ?

Answer 1

What kind of integration (what functions)?

Answer 2

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...

Answer 3

\[1)\int\limits_{}^{}sinf(x).f'(x)dx=-cosf(x)+c\]
\[2)\int\ Cosf(x).f'(x)dx=Sinf(x)+c\]
\[3)\int\limits_{}^{}\tan f(x).f'(x)dx=lnsecf(x)+c\]
\[4)\int\ Secf(x).f'(x)dx=\ln \left[ secf(x)+tanf(x) \right]\]
\[5)\int\limits_{}^{}Cotf(x).f'(x)dx=lnsinx+c\]
\[6)\int\limits_{}^{} Cosec f(x).f'(x)dx=\ln(cosecf(x)-cotf(x) ) +c\]
\[7)\int\ Sec^2f(x).f'(x)dx=tanf(x)+c\]
\[8)\int\limits_{}^{}Cosec^2f(x).f'(x)dx=-Cot f(x)+c\]
\[9)\int\limits_{}^{}Sec f(x).Cosecf(x).f'(x)dx=Secf(x)\]


I do remember some of these .

Answer 4

u want more formulas?

Answer 5

http://openstudy.com/users/hartnn#/updates/50960518e4b0d0275a3ccfba

Answer 6

Yeah thanks.

Answer 7

@hartnn

What about the tricks ?


I think i forgot them

When we have a cycle from 0 to pi i guess.

Answer 8

yeah...
from 0 to 2pi, integration of sin and cos is 0....

Answer 9

do u want it properly in latex from, or in words form ??

Answer 10

@hartnn

Latex form with some examples please.

Answer 11

have patience, it will take time...

Answer 12

Yeah lol thanks i am waiting :)

Answer 13

\(\color {red} {\text{ If m,n are Integers } \\ \text{Set I : } \\\int \limits_0^{2 \pi} \sin nx = 0 \\\int \limits_0^{2 \pi} \cos nx = 0 \\\int \limits_0^{2 \pi} \sin nx . \cos nx = 0 \\ \int \limits_0^{2 \pi} \sin nx \sin mx = 0 [m \ne n] \\\int \limits_0^{2 \pi} \cos nx \cos mx = 0 [m \ne n]}\)

Answer 14

\(\color{red}{\text{Set II :}\\ \int \limits_0^{2 \pi}\sin^2nx =\pi \\\int \limits_0^{2 \pi}\cos^2nx =\pi }\)

Answer 15

sorry i am missing dx everywhere

Answer 16

\(\color {red}{\\\int \limits_0^{\color{blue }{n}\pi}\sin^2nx=\color{blue}{n}\pi/2 \\ }\)
\(\color {red}{\\\int \limits_0^{\color{blue }{n}\pi}\cos^2nx=\color{blue}{n}\pi/2 \\ }\)

Answer 17

\(\color{red}{\int \limits_0^\pi\sin mx.\sin nx=0(m \ne n)}\)
\(\color{red}{\int \limits_0^\pi\cos mx.\cos nx=0(m \ne n)}\)

Answer 18

thats all i have...

Answer 19

Yaar @hartnn

Is mai koi odd or even ka scene bhi hota hai na ?

Answer 20

generally, if the function f(x) is odd, then
\(\huge \int \limits_{-a}^af(x)=0 \)
if the function f(x) is even
\(\huge \int \limits_{-a}^af(x)=2\int \limits_{0}^af(x) \)

Answer 21

@hartnn

Set hai,Thanks a lot :)

Answer 22

@hartnn

Acha aik example show krdo mujhe ?

Answer 23

example for which formula ?

Answer 24

Jo odd or even hai na uss kai liyee.

Answer 25

u know how to find even / odd function ?

Answer 26

\(\huge \int \limits_{-a}^a(x^3-x) dx=... \\ \huge \int \limits_{-\pi/2}^{\pi/2}\sin^3x dx=...\)

Answer 27

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.

Answer 28

\(\huge \int \limits_{-\pi}^{\pi}\sin2x.\sin5x dx=.... \\\huge \int \limits_{-a}^ax^4+x^2+1.dx=....\)

Answer 29

sin (-x) = -sin x <----odd
cos(-x) = cos x <----even

Answer 30

Oh sahi hai :)

Answer 31

Acha or hyperbolic function ka kia hota hai integration mai ?

Answer 32

mere link me hai, hyperbolics....

Answer 33

Chalo let me check

Answer 34

thanks a lot :)

Answer 35

got it ?
for properties of definite integrals
http://www.pinkmonkey.com/studyguides/subjects/calc/chap7/c0707501.asp
12th one is my fav....

Answer 36

challenge Q, if any1's interested ..... PROVE
\(\int\limits_{0}^{\pi} \ln \sin(x)=-\pi \ln(2)\)
i've solved that on OS...