Evaluate ∫$$sin$$⁡$$2xsin$$⁡$$3xdx$$

Correct option is 3sin⁡x2−sin⁡5x10+C

Questions

$Evaluate \int \sin 2 x \sin 3 x d x$

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sin⁡x2−sin⁡5x5+C

sin⁡2x2−sin⁡5x10+C

sin⁡x2−sin⁡5x10+C

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detailed solution

Correct option is C

∫sin⁡2xsin⁡3xdx=12∫2sin⁡3xsin⁡2xdx=12∫[cos⁡(3x−2x)−cos⁡(3x+2x)]dx [∵2sin⁡Asin⁡B=cos⁡(A−B)−cos⁡(A+B)]=12∫[cos⁡x−cos⁡5x]dx=12∫cos⁡xdx−12∫cos⁡5xdx=12sin⁡x−12sin⁡5x5+C=sin⁡x2−sin⁡5x10+C

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Evaluate ∫sin⁡2xsin⁡3xdx

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$Evaluate \int \sin 2 x \sin 3 x d x$