Test Index

NCERT Class XII Mathematics Chapter - - Solutions

Show Para  Hide Para 
..... Miscellaneous Exercise .....
Integrate the functions in Exercises 229 to 252.
© examsnet.com
Question : 235 of 271
Marks: +1, -0
sin⁡xsin⁡(x−a)\frac{\sin x}{\sin (x-a)}
Solution:  
Let I=∫sin⁡xsin⁡(x−a)dxI=\int\frac{\sin x}{\sin (x-a)}dx
=∫sin⁡((x−a)+a)sin⁡(x−a)dx=\int\frac{\sin((x-a)+a)}{\sin(x-a)}dx
=∫sin⁡(x−a)cos⁡a+cos⁡(x−a)sin⁡asin⁡(x−a)=\int\frac{\sin(x-a)\cos a+\cos(x-a)\sin a}{\sin(x-a)}
=cos⁡a∫dx+sin⁡a∫cot⁡(x−a)dx=\cos a\int dx+\sin a\int\cot(x-a)dx
=xcos⁡a+sin⁡alog⁡sin⁡(x−a)+C= x \cos a + \sin a \log \sin(x - a) + C
© examsnet.com
Go to Question:
Prev Question
Next Question
Advertisements