\$\$int_-fracpi6^fracpi6left(int_0^6cos(3 heta) r dr ight) d heta\$\$

And I obtained an answer of \$frac112pi\$. At the finish of the difficulty, I got\$\$ frac14left(frac16pi + 6sinleft(fracpi6^2 ight) - frac14left(frac-pi6+6sin(-pi) ight) ight) \$\$

which need to be \$frac112pi\$ which I am unsure if it is best or not.

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\$\$ int_-fracpi6^fracpi6left(int_0^6cos(3 heta) r katifund.orgrm dr ight) katifund.orgrm d heta\$\$ \$\$=18int_-fracpi6^fracpi6cos^2(3 heta) katifund.orgrm d heta\$\$Because the integrand also is an also feature, we have\$\$36int_0^fracpi6cos^2(3 heta) katifund.orgrm d heta\$\$Now we deserve to usage the fact that\$\$int cos^2(ax) katifund.orgrm dx=fracx2+frac14asin(2ax)+C\$\$Wbelow in our case \$a=3\$, therefore\$\$36left(fracpi12+frac112sinleft(pi ight) ight)=frac36pi12=3pi\$\$

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