If ∫ s i n ( x − α ) s i n x d x = A x + B lo g sin ( x − α ) + C , then value of ( A , B ) is

Put x − α = t ⇒ ∫ s i n t s i n ( α + t ) d t = sin α ∫ cot t d t + cos α ∫ d t = cos α ( x − α ) + sin α ln ∣ sin t ∣ + c A = cos α , B = sin α

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Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationSubstitutionMedium2 minPYQ_2004

MathematicsMediumsingle choice

If $\int \frac{s i n x}{s i n ( x - α )} d x = A x + B lo g sin (x - α) + C$ , then value of $(A, B)$ is

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Solution:

Put $x - α = t$ $\Rightarrow \int \frac{s i n ( α + t )}{s i n t} d t = sin α \int cot t d t + cos α \int d t$ $= cos α (x - α) + sin α ln ∣ sin t ∣ + c$ $A = cos α, B = sin α$

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Substitution

⏱ 2mℹ️ Source: PYQ_2004

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