Evaluate the following integrals. \int sin^{2}0 \cos^{5} 0d0

foass77W 2021-02-16 Answered
Evaluate the following integrals.
sin20cos50d0
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Expert Answer

casincal
Answered 2021-02-17 Author has 82 answers
Step 1
Consider the provided integral,
sin20cos50d0
Evaluate the following integrals.
Using the trigonometric identity,
sin2(0)cos5(0)d0=(1sin2(0))2cos(0)sin2(0)d0
Apply u-Substitution method,
u=sin0du=cos0d0
Step 2
Therefore,
sin2(0)cos5(0)d0=u2(1u2)2du
=u22u4+u6du
=u2du2u4du+u6du
=u332u55+u77+C
Substitute back,
sin2(0)cos5(0)d0=sin3032sin505+sin707+C
Hence.
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