The value of 2 ∫ s i n ( x − 4 π ) s i n x d x is

2 ∫ sin ( x − 4 π ) sin x d x = 2 ∫ sin ( x − 4 π ) sin ( x − 4 π + 4 π ) d x = 2 ∫ ( cos 4 π + cot ( x − 4 π ) sin 4 π ) d x = ∫ d x + ∫ cot ( x − 4 π ) d x = x + ln sin ( x − 4 π ) + c .

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Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationSubstitutionEasy2 minPYQ_2008

MathematicsEasysingle choice

The value of $2 \int \frac{s i n x d x}{s i n ( x - \frac{π}{4} )}$ is

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Answer:

Solution:

$2 \int \frac{sin x d x}{sin ( x - \frac{π}{4} )} = 2 \int \frac{sin ( x - \frac{π}{4} + \frac{π}{4} ) d x}{sin ( x - \frac{π}{4} )} = 2 \int (cos \frac{π}{4} + cot (x - \frac{π}{4}) sin \frac{π}{4}) d x = \int d x + \int cot (x - \frac{π}{4}) d x = x + ln sin (x - \frac{π}{4}) + c .$

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Substitution

⏱ 2mℹ️ Source: PYQ_2008

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