Javascript is required
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JEE Main 2021 (Online) 16th March Morning Shift
Numerical  +4  -1
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 _________.
2
JEE Main 2021 (Online) 16th March Morning Shift
Numerical  +4  -1
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 ___________.
Let the normals at all the points on a given curve pass through a fixed point (a, b). If the curve passes through (3, $$-$$3) and (4, $$-$$2$$\sqrt 2$$), and given that a $$-$$ 2$$\sqrt 2$$ b = 3,