Indefinite Integral

Find the following integral:

    \[\int \sin {x} \sin {2x} \, \mathrm{d}x\]

Answer:

Using the double-angle formula,

    \[\sin {2x}= 2\sin{x} \cos{x}\]

So,

    \[\sin{x} \sin {2x}= \sin{x} \cdot 2\sin{x} \cos{x} = 2 \sin^{2}{x} \cos{x}\]

    \[\frac{2}{3}\sin^{3}{x}+C\]

where C is an arbitrary constant.

Source: R.L. Rosenberg. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Additional Exercises in Integration: Question (xi))

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

Leave a Reply