Integration techniques

Question code: 2a634

Question 0803

Find the exact value of 034πsin6xcos6xdx.{\displaystyle \int_0^{\frac{3}{4} \pi} \sin 6 x \cos 6 x \, \mathrm{d}x.} Hence find the exact value of 034π(sin6x+cos6x)2dx.{\displaystyle \int_0^{\frac{3}{4} \pi} (\sin 6 x + \cos 6 x)^2 \, \mathrm{d}x.}
[6]
Answer
034πsin6xcos6xdx=112{\displaystyle \int_0^{\frac{3}{4} \pi} \sin 6 x \cos 6 x \, \mathrm{d}x = \frac{1}{12}}.
034π(sin6x+cos6x)2dx=16+34π{\displaystyle \int_0^{\frac{3}{4} \pi} (\sin 6 x + \cos 6 x)^2 \, \mathrm{d}x = \frac{1}{6} + \frac{3}{4} \pi}.
Question code: 2a634