If the value of $$\large 34 \times \frac{ \int\limits_{0}^{\pi}(\sin x)^{3\sqrt{2}+3} dx }{ \int\limits_{0}^{\frac{ \pi }{ 2 }} (\cos x)^{3\sqrt{2} -3} dx } = a \sqrt{2} + b$$
for integers a,b. $$\ \text{What is the value of} ~~~a + b ~~~?$$

Question

If the value of $$\large 34 \times \frac{ \int\limits_{0}^{\pi}(\sin x)^{3\sqrt{2}+3} dx }{ \int\limits_{0}^{\frac{ \pi }{ 2 }} (\cos x)^{3\sqrt{2} -3} dx  } = a \sqrt{2}  + b$$
for integers a,b. $$\ \text{What is the value of} ~~~a + b ~~~?$$

usukidoll · Answer

the value is I quit...this is crazy

shamil98 · Answer

lol xD

anonymous · Answer

Might want to use McLaurin series.

anonymous · Answer

How accurate of an answer do you want? You could use a series expansion or other approximate method (Brute force numerical methods, etc.)

anonymous · Answer

Grabs pencil + piece of paper, cracks knuckles...here we go..

anonymous · Answer

$$
\sin(x) = \sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)}x^{2k+1}
$$

anonymous · Answer

I'm not sure how much this will help exactly.

nincompoop · Answer

wio is giving us more work! laughing out loud jaykay

anonymous · Answer

Besides the constraint on a and b being integers, what other information is available to solve for two unknowns with only one equation?

anonymous · Answer

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