# Worst impact an Earthquake can have!

Calculus Level 5

Mayank and Akul are badly affected by the earthquake.

Mayank is trying a calculus question:-

Calculate $$S=\displaystyle\int_{0}^{\frac { \pi }{ 2 }}\sin { ({ x }^{ 2 }) } dx$$

Akul asks Mayank to give him an algebra problem to solve. Mayank gives him:-

$$\displaystyle\sum_{r=0}^n a_{r} { (x-S+1) }^{ r } = \displaystyle\sum_{r=0}^n b_{r} { (x-S) }^{ r }$$ where n=2k for some k$$\in\mathbb{N}$$

and $$a_{t}$$=1 for all t$$\ge$$k

If $$b_{k} = \frac { (\alpha k+\beta )! }{ (\gamma k+\delta )!(\mu k+\lambda )! }$$

Find the remainder when ( $$\alpha +\beta +\gamma +\delta +\mu +\lambda$$ ) is divided by 97.

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