If y = y(x) is the solution of the differential equation,

$${{dy} \over {dx}} + 2y\tan x = \sin x,y\left( {{\pi \over 3}} \right) = 0$$, then the maximum value of the function y(x) over R is equal to:

Let the curve y = y(x) be the solution of the differential equation, $${{dy} \over {dx}}$$ = 2(x + 1). If the numerical value of area bounded by the curve y = y(x) and x-axis is $${{4\sqrt 8 } \over 3}$$, then the value of y(1) is equal to _________.

Let f : R $$ \to $$ R be a continuous function such that f(x) + f(x + 1) = 2, for all x$$\in$$R.

If $${I_1} = \int\limits_0^8 {f(x)dx} $$ and $${I_2} = \int\limits_{ - 1}^3 {f(x)dx} $$, then the value of I₁ + 2I₂ is equal to ____________.

If the normal to the curve y(x) = $$\int\limits_0^x {(2{t^2} - 15t + 10)dt} $$ at a point (a, b) is parallel to the line x + 3y = $$-$$5, a > 1, then the value of | a + 6b | is equal to ___________.