Integrate the following functions w.r.t. x : sin(x-a)cos(x +b) - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : `sin(x - a)/cos(x  + b)`

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Solution

Let I = `intsin(x - a)/cos(x + b).dx`

= `int(sin[(x + b) - (a  + b)])/cos(x + b).dx`

= `int[sin(x + b) cos(a + b) - cos(x + b)sin(a + b))/cos(x + b).dx`

= `int[(sin(x + b) cos(a + b))/cos(x + b) - (cos(x + b)sin(a + b))/cos(x + b)].dx`

= `cos (a + b) int tan (x + b) dx - sin (a + b) int 1dx`

= cos (a + b) log | sec (x + b) | – x sin (a + b) + c.

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Chapter 3: Indefinite Integration - Exercise 3.2 (A) [Page 110]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Exercise 3.2 (A) | Q 2.03 | Page 110

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