If ∫ 2 c o s x − s i n x + λ c o s x + s i n x − 2 d x = A ℓ n | c o s x + s i n x − 2 | + B x + C . Then the ordered triplet A , B , λ is Options: A . &nbsp ( 1 2 , 3 2 , − 1 ) B . &nbsp ( 3 2 , 1 2 , − 1 ) C . &nbsp ( 1 2 , − 1 , − 3 2 ) D . &nbsp ( 3 2 , − 1 , − 1 2 )

Answer: Option B : B d d x ( A | c o s x + s i n x − 2 | + B x + C ) = A c o s x − s i n x c o s x + s i n x − 2 + B = A c o s x + B c o s x − A s i n x + B s i n x − 2 B c o s x + s i n x − 2 ∴ A + B = 2 , A + B = − 1 , − 2 B = λ ∴ A = 3 2 , B = 1 2 , λ = − 1

If ∫2cosx−sinx+λcosx+sinx−2dx=Aℓn|cosx+sinx&

Discussion Forum : Indefinite Integration

Question -

If $\int \frac{2 c o s x - s i n x + λ}{c o s x + s i n x - 2} d x = A ℓ n | c o s x + s i n x - 2 | + B x + C$ . Then the ordered triplet $A, B, λ$ is

Options:

A .

(\frac{1}{2}, \frac{3}{2}, - 1)

B .

(\frac{3}{2}, \frac{1}{2}, - 1)

C .

(\frac{1}{2}, - 1, - \frac{3}{2})

D .

(\frac{3}{2}, - 1, - \frac{1}{2})

Answer: Option B
:
B

\frac{d}{d x} (A | c o s x + s i n x - 2 | + B x + C) = A \frac{c o s x - s i n x}{c o s x + s i n x - 2} + B = \frac{A c o s x + B c o s x - A s i n x + B s i n x - 2 B}{c o s x + s i n x - 2} ∴ A + B = 2, A + B = - 1, - 2 B = λ ∴ A = \frac{3}{2}, B = \frac{1}{2}, λ = - 1

Was this answer helpful ?

Next Question

Discussion Forum : Indefinite Integration

Submit Your Solution hear: