Question
If the integral 
then an equal to
-
-1
-
-2
-
1
-
2
Solution
D.
2
Now, let us assume that I,
Multiplying by cos x in numerator and denominator, we get
This special integration requires special substitution of type
N' = A (D') +
⇒ Let 5 sin x = (A + 2B) sin x + (B- 2A) cos x
Comapring the coefficients of sin x and cosx,
we get
A +2B =5 and B- 2A = 0
Solving the above two equations in A and B
we get
A = 1 an B= 2
⇒ 5 sin x = ( sin x - 2 cos x)+ 2 (cos x + 2 sin x)
where k is the constant of integration. Now, by comparing the value of l in eq. (i) and (ii) we get a = 2
This special integration requires special substitution of type
N' = A (D') +
⇒ Let 5 sin x = (A + 2B) sin x + (B- 2A) cos x
Comapring the coefficients of sin x and cosx,
we get
A +2B =5 and B- 2A = 0
Solving the above two equations in A and B
we get
A = 1 an B= 2
⇒ 5 sin x = ( sin x - 2 cos x)+ 2 (cos x + 2 sin x)
where k is the constant of integration. Now, by comparing the value of l in eq. (i) and (ii) we get a = 2
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