Integrate the following functions w.r.t. x : 3cos2x.sin2x - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`

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Solution

let I = `int 3^(cos^2x) sin2x dx`
Put cos2x = t

∴ `[2 cos x d/dx (cos x)]dx` = dt

∴ – 2 sin x cos x dx = dt
∴ sin 2x dx = – dt

I = `- int3^t dt`

= `-(1)/(log3).3^t + c`

= `-(1)/(log3).3^(cos^2x) + c`.

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

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Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Exercise 3.2 (A) | Q 2.15 | Page 110

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