|

Integral Calculus

Hot goIITian

 Joined: 18 Jan 2012 Post: 147
20 Feb 2012 15:34:56 IST
1 People liked this
2
438
Integration Challenge-4!!
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Integral Calculus

Integration Challenge-4!!

Integrate:

Click on View post at the top right corner of this post if not visible.

Blazing goIITian

Joined: 19 Jan 2008
Posts: 1139
20 Feb 2012 17:39:15 IST
0 people liked this

[img]http://latex.codecogs.com/gif.latex?\hspace{-16}\mathbf{\int\frac{x^2}{(x\cos%20x-\sin%20x).(x\sin%20x+\cos%20x)}dx}$\\\\\\%20Now%20We%20Can%20Write%20$\mathbf{x^2=x^2(\sin^2%20x+\cos^2%20x)}$\\\\\\%20So%20$\mathbf{x^2=(x\cos%20x-\sin%20x).\frac{d}{dx}(x\sin%20x+\cos%20x)}$\\\\\\%20$\mathbf{-(x\sin%20x+cos%20x).\frac{d}{dx}(x\cos%20x-\sin%20x)}$\\\\\\%20So%20$\mathbf{x^2=(x\cos%20x-\sin%20x).(x\cos%20x)-(x\cos%20x+\sin%20x)(-x\sin%20x)}$\\\\\\%20So%20Original%20Integral%20Integral%20Convert%20into%20\\\\\\%20$\mathbf{=\int\frac{(x\cos%20x-\sin%20x).(x\cos%20x)-(x\cos%20x+\sin%20x)(-x\sin%20x)}{(x\cos%20x-\sin%20x).(x\sin%20x+\cos%20x)}}$\\\\\\%20$\mathbf{=\ln%20\left|x\sin%20x+\cos%20x%20\right%20|-\ln\left|x\cos%20x-\sin%20x\right|+C}$\\\\\\%20So%20$\mathbf{\int\frac{x^2}{(x\cos%20x-\sin%20x).(x\sin%20x+\cos%20x)}dx=\ln%20\left|\frac{x\sin%20x+\cos%20x%20}{x\cos%20x-\sin%20x}\right|+C}\$[img]

Blazing goIITian

Joined: 19 Jan 2008
Posts: 1139
20 Feb 2012 17:39:58 IST
1 people liked this

$\hspace{-16}\mathbf{\int\frac{x^2}{(x\cos x-\sin x).(x\sin x+\cos x)}dx}\\\\\\ Now We Can Write \mathbf{x^2=x^2(\sin^2 x+\cos^2 x)}\\\\\\ So \mathbf{x^2=(x\cos x-\sin x).\frac{d}{dx}(x\sin x+\cos x)}\\\\\\ \mathbf{-(x\sin x+cos x).\frac{d}{dx}(x\cos x-\sin x)}\\\\\\ So \mathbf{x^2=(x\cos x-\sin x).(x\cos x)-(x\cos x+\sin x)(-x\sin x)}\\\\\\ So Original Integral Integral Convert into \\\\\\ \mathbf{=\int\frac{(x\cos x-\sin x).(x\cos x)-(x\cos x+\sin x)(-x\sin x)}{(x\cos x-\sin x).(x\sin x+\cos x)}}\\\\\\ \mathbf{=\ln \left|x\sin x+\cos x \right |-\ln\left|x\cos x-\sin x\right|+C}\\\\\\ So \mathbf{\int\frac{x^2}{(x\cos x-\sin x).(x\sin x+\cos x)}dx=\ln \left|\frac{x\sin x+\cos x }{x\cos x-\sin x}\right|+C}$

 Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a avatar to have your pictures show up by your comment If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

## For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
 Altitude - 16545 m Post - 7958
2. Himanshu
 Altitude - 10925 m Post - 3836
3. Hari Shankar
 Altitude - 10085 m Post - 2217
4. edison
 Altitude - 10825 m Post - 7804
5. Sagar Saxena
 Altitude - 8635 m Post - 8064
 Altitude - 6330 m Post - 1958

Physics

Topics

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone