Integrate with sin cos #2

Calculus Level 5

$\large{\displaystyle \int^{\frac{\pi}{4}}_{0} (\sin 2 \theta)^{\frac{5}{2}} (\sin \theta+\cos \theta) \, d\theta=\frac{A}{B} \pi}$

If $A$ and $B$ are coprime integers, find $A+B$ .

Try my set

The answer is 37.

1 solution

Tanishq Varshney
Sep 11, 2015

sorry i missed out $d \theta$ in one of the steps

I did it this way: Because $\sin(2\theta) = 1- ( \cos\theta - \sin\theta)^2$ , so I let $y = \cos\theta - \sin\theta$ . Then for integration of $\cos^6 x$ , I do reduction formula (Wallis Product): 5!!/6!! * pi/2 = 5pi/32.

Nice question by the way!

Pi Han Goh - 5 years, 9 months ago

Integrate with sin cos #2

Try my set

The answer is 37.

1 solution

0 pending reports