Let T be the tangent to the ellipse E : x² + 4y² = 5 at the point P(1, 1). If the area of the region bounded by the tangent T, ellipse E, lines x = 1 and x = $$\sqrt 5 $$ is $$\alpha$$$$\sqrt 5 $$ + $$\beta$$ + $$\gamma$$ cos^$$-$$1$$\left( {{1 \over {\sqrt 5 }}} \right)$$, then |$$\alpha$$ + $$\beta$$ + $$\gamma$$| is equal to ______________.

Let P(x) be a real polynomial of degree 3 which vanishes at x = $$-$$3. Let P(x) have local minima at x = 1, local maxima at x = $$-$$1 and $$\int\limits_{ - 1}^1 {P(x)dx} $$ = 18, then the sum of all the coefficients of the polynomial P(x) is equal to _________.

Let f(x) and g(x) be two functions satisfying f(x²) + g(4 $$-$$ x) = 4x³ and g(4 $$-$$ x) + g(x) = 0, then the value of $$\int\limits_{ - 4}^4 {f{{(x)}^2}dx} $$ is

Let $${I_n} = \int_1^e {{x^{19}}{{(\log |x|)}^n}} dx$$, where n$$\in$$N. If (20)I₁₀ = $$\alpha$$I₉ + $$\beta$$I₈, for natural numbers $$\alpha$$ and $$\beta$$, then $$\alpha$$ $$-$$ $$\beta$$ equals to ___________.