262if we allowed to approximate π to 3.14 (exactly) ,
then i think k = 150
\hspace{-16}$Let $\bf{a\in \mathbb{R}}$. If the value of $\bf{\int_{-\pi+a}^{3\pi+a}\mid x-a-\pi\mid\sin \left(\frac{x}{2}\right)dx=-16}$\\\\\\ Then Sum of all Integer value of $\bf{a}$ in $\bf{\left[0,314\right]}$ is $\bf{k\pi}$.\;\;Then $\bf{\mathbb{K}=}$
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71I think the values of ' a ' that are suitable for this purpose within the limits [0,100Î ] , after rounding of for Î =3.14 are 0,4Î ,8Î ,...,100 Î . Whose sum would be 1300Î
So I think , I would not agree with your answer.
71If you take it to be in exact manner, then neither of us would give correct answer :P
By the way, what are those integer values that you are getting.
71Even if we take Î =3.14 , 57Î = 178.98.
ANyways, Lets see what man111 has to post!
1708Thanks for Nice Discussion Aditiya and Vivek..
But I have no solution.
I also Getting The Same thing as Vivek Getting.