## hba 2 years ago Can anyone help me i almost forgot what integration is ?

1. agent0smith

What kind of integration (what functions)?

2. agent0smith

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...

3. 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 .

4. hartnn

u want more formulas?

5. hartnn
6. hba

Yeah thanks.

7. hba

@hartnn What about the tricks ? I think i forgot them When we have a cycle from 0 to pi i guess.

8. hartnn

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

9. hartnn

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

10. hba

@hartnn Latex form with some examples please.

11. hartnn

have patience, it will take time...

12. hba

Yeah lol thanks i am waiting :)

13. hartnn

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

14. hartnn

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

15. hartnn

sorry i am missing dx everywhere

16. hartnn

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

17. hartnn

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

18. hartnn

thats all i have...

19. hba

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

20. hartnn

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

21. hba

@hartnn Set hai,Thanks a lot :)

22. hba

@hartnn Acha aik example show krdo mujhe ?

23. hartnn

example for which formula ?

24. hba

Jo odd or even hai na uss kai liyee.

25. hartnn

u know how to find even / odd function ?

26. hartnn

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

27. 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.

28. hartnn

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

29. hartnn

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

30. hba

Oh sahi hai :)

31. hba

Acha or hyperbolic function ka kia hota hai integration mai ?

32. hartnn

33. hba

Chalo let me check

34. hba

thanks a lot :)

35. hartnn

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

36. hartnn

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