1
JEE Main 2021 (Online) 31st August Morning Shift
Numerical
+4
-1
Let [t] denote the greatest integer $$\le$$ t. Then the value of

$$8.\int\limits_{ - {1 \over 2}}^1 {([2x] + |x|)dx}$$ is ___________.
2
JEE Main 2021 (Online) 31st August Morning Shift
Numerical
+4
-1
If $$x\phi (x) = \int\limits_5^x {(3{t^2} - 2\phi '(t))dt}$$, x > $$-$$2, and $$\phi$$(0) = 4, then $$\phi$$(2) is __________.
3
JEE Main 2021 (Online) 26th August Evening Shift
Numerical
+4
-1
Let a and b respectively be the points of local maximum and local minimum of the function f(x) = 2x3 $$-$$ 3x2 $$-$$ 12x. If A is the total area of the region bounded by y = f(x), the x-axis and the lines x = a and x = b, then 4A is equal to ______________.
4
JEE Main 2021 (Online) 26th August Morning Shift
Numerical
+4
-1
The area of the region $$S = \{ (x,y):3{x^2} \le 4y \le 6x + 24\}$$ is ____________.
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