Evaluate the following : ∫14+3cos2x.dx - Mathematics and Statistics

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Sum

Evaluate the following : `int (1)/(4 + 3cos^2x).dx`

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Solution

Let I = `int (1)/(4 + 3cos^2x).dx`

Dividing both numerator and denominator by cos2x, we get

I = `int (sec^2x)/(4sec^2 x + 3).dx`

= `int (sec^2x)/(4(1 + tan^2x) + 3).dx`

= `int (sec^2x)/(4tan^2x + 7).dx`
Put tan x = t
∴ sec2x dx = dt

I = `int dt/(4t^2 + 7)`

= `int dt/((2t)^2 + (sqrt(7))^2`

= `(1)/sqrt(7)tan^-1 ((2t)/sqrt(7)).(1)/(2) + c`

= `(1)/(2sqrt(7))tan^-1 ((2tanx)/sqrt(7)) + 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 1.18 | Page 123

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