help@askiitians.com

+91-705-589-3577

Integral Calculus> evaluate the following integral ∫ sin(x –...

question mark

evaluate the following integral
∫ sin(x – a) / sin(x – b) dx

taniska , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{sin(x-a)}{sin(x-b)}dx$
$I = \int \frac{sin(x-b+b-a)}{sin(x-b)}dx$
$I = \int \frac{sin((x-b)+(b-a))}{sin(x-b)}dx$
$I = \int \frac{sin(x-b)cos(b-a)+cos(x-b)sin(b-a)}{sin(x-b)}dx$
$I = \int [cos(b-a) + \frac{cos(x-b)sin(b-a)}{sin(x-b)}]dx$
$I = \int cos(b-a)dx + \int \frac{cos(x-b)sin(b-a)}{sin(x-b)}dx$
$I = xcos(b-a) + sin(b-a)\int \frac{cos(x-b)}{sin(x-b)}dx$
$sin(x-b) = t$
$cos(x-b)dx = dt$
$I = xcos(b-a) + sin(b-a)\int \frac{1}{t}dt$
$I = xcos(b-a) + sin(b-a)log(t)+c$
$I = xcos(b-a) + sin(b-a)log(sin(x-b))+c$

Last Activity: 11 Years ago

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

The area of a square field is 640000cm².what is its area in hectares

integral calculus

1 Answer Available

Last Activity: 3 Years ago

Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request

integral calculus

1 Answer Available

Last Activity: 3 Years ago

Using laplace transform, solve d²y/dt²+ dy/dt = t² +2t given that y=4 and y’=-2 and t=0

integral calculus

1 Answer Available

Last Activity: 3 Years ago

If 4th term of an A.p is zero, show that the 8th term is double the 6th term

integral calculus

1 Answer Available

Last Activity: 4 Years ago

View all Questions