# Originality!!

Calculus Level 5

The equation of the curve $$y$$=$$f(x)$$.The tangents at :-

(1,$$f(1)$$),(2,$$f(2)$$) ,and(3,$$f(3)$$) makes angle $$\dfrac{\pi}{6}$$,$$\dfrac{\pi}{3}$$ and $$\dfrac{\pi}{4}$$ respectively with the positive direction of $$x$$- axis.Then the value of

$$\displaystyle\int_{2}^{3}$$$$f'(x)$$$$f"(x)$$$$dx$$+ $$\displaystyle\int_{1}^{3}$$$$f"(x)$$$$dx$$ can be expressed as

$$\dfrac{-1}{a}$$ find the value of $$a$$.

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