Integrate the following functions w.r.t. x : ∫1cosx-sinx.dx - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`

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Solution

Let I = `int (1)/(cosx - sinx).dx`

Dividing each term by `sqrt(1^2 + (-1)^2) = sqrt(2)`, we get

I = `(1)/sqrt(2) int (1)/(cosx. 1/sqrt(2) - sinx. 1/sqrt(2)).dx`

= `1/sqrt(2) int (1)/(cosx  . cos  pi/(4) - sin x. sin  pi/(4)).dx`

= `1/sqrt(2) int (1)/(cos(x + pi/4)).dx`

= `1/sqrt(2) int sec(x + pi/4).dx`

= `1/sqrt(2)log|sec(x + pi/4) + tan(x + pi/4)| + c`.

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Chapter 3: Indefinite Integration - Exercise 3.2 (B) [Page 123]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Exercise 3.2 (B) | Q 2.8 | Page 123

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