# Inverse is Integral in Maths!

Calculus Level 3

$$\displaystyle a = \int_0^{1} \arctan (1- x + x^2) \, dx$$

Find the other root of a quadratic polynomial which has one of its roots as $$a$$ and has its minimum at $$\ln \sqrt{2}$$.

Details and Clarifications:

• A number $$p$$ is said to be a root of a polynomial $$f(x)$$ if $$f(p) = 0$$.

• $$\displaystyle \arctan p$$ is the same as $$\tan^{-1} p$$.

• $$\displaystyle \ln p$$ is the same as $$\log_e p$$.

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