Integrate the functions: cosx1+sinx - Mathematics

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Sum

Integrate the functions:

`cos x /(sqrt(1+sinx))`

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Solution

Let `I = int (cos x)/sqrt(1 + sin x)` dx

Put 1 + sin x = t

cos x dx = dt

∴ `I = int dt/sqrt(1 + t) = (1 + t)^(1/2 +1)/(1/2 + 1) + C`

`= 2 (1 + t)^(1/2) + C`

`= 2 sqrt(1 + sin x + C)`

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Chapter 7: Integrals - Exercise 7.2 [Page 305]

APPEARS IN

NCERT Mathematics Class 12
Chapter 7 Integrals
Exercise 7.2 | Q 28 | Page 305

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