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

Question

Integrate the following functions w.r.t. x : $3^{\cos^{2} x} \sin 2 x$

Sum

Solution

let I = $\int 3^{\cos^{2} x} \sin 2 x d x$
Put cos²x = t

∴ $[2 \cos x \frac{d}{d x} (\cos x)] d x$ = dt

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

I = $- \int 3^{t} d t$

= $- \frac{1}{\log 3} {.3}^{t} + c$

= $- \frac{1}{\log 3} {.3}^{\cos^{2} x} + c$ .

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Methods of Integration: Integration by Substitution

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

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Chapter 3 Indefinite Integration
Exercise 3.2 (A) | Q 2.15 | Page 110

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

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