Integrate the following functions w.r.t. x : sin5x.cos8x - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : sin5x.cos8x

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Solution

Let I = `int sin^5xcos^8xdx`

=`int sin^4xcos^8xsinxdx`

= `int(1 - cos^2x)^2 cos^8xsinxdx`
Put cos x = t
∴ – sin x dx = dt
∴ sin x dx = – dt
I = `- int(1 - t^2)^2t^8 dt`

= `- int(1 - 2t^2 + t^4)t^8 dt`

= `- int (t^8 - 2t^10 + t^12)dt`

= `- int t^8dt + 2 intt^10 dt - int t^12 dt`

= `- t^9/(9) + 2(t^11/11) - t^13/(13) + c`

= `-(1)/(9)cos^9x + (2)/(11)cos^11x - (1)/(13)cos^13x + 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 2.14 | Page 110

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