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Find ∫e
^{
x
}
√(1 + sin β‘2x )/(1 + cos β‘2x ) dx

Download Sample Paper of Class 12 here https://www.teachoo.com/cbse/sample-papers/

Last updated at May 29, 2018 by Teachoo

Download Sample Paper of Class 12 here https://www.teachoo.com/cbse/sample-papers/

Transcript

Question 9 Find 1 ^ (1 + sin 2 )/(1 + cos 2 ) dx 1 ^ (1 + 2 )/(1 + 2 ) dx Putting sin 2x = 2 sin x cos x cos 2x = 2 cos2 x 1 = 1 ^ (1 + 2 sin cos )/(1 + (2 cos^2 1)) dx = 1 ^ (1 + 2 sin cos )/(2 cos^2 ) dx Putting 1 = sin2 x + cos2 x = 1 ^ (sin^2 + cos^2 + 2 sin cos )/(2 cos^2 ) dx = 1 (( + )^2 )/(2 2 )dx = 1/2 1 ^ (sin /( 2 )+cos /( 2 )) = 1/2 1 ("sec sec tan x " ) = 1/2 ^ sec x + c [ ^ ( ( )+ ^ ( )) = ^ ( )+ ] Using (a + b)2 = a2 + b2 + 2ab where a = sin x , b = cos x = 1 ^ (( + )^2 )/(2 2 ) dx = 1/2 1 ^ (( + ))/ 2 dx = 1/2 1 ^ (sin /( 2 )+cos /( 2 )) = 1/2 1 ^ (sin /( ) 1/cos +1/cos ) = 1/2 1 ^ (tan sec +sec ) = 1/2 1 ^ (sec +tan sec ) Using 1 ^ ( ( )+ ^ ( )) = ^ ( )+ Where f(x) = sec x = / ^ sec x + c

Paper Summary

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Question 8

Question 9 You are here

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Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Class 12

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.