( _ ,0 ^ ,a x ,dx ) (a + 4), then - Vidyadip

MCQ

$\left( {\int_{\,0}^{\,a} {x\,dx} } \right) \le (a + 4),$ then

A
$ 0 \le a \le 4$
✓
$ - 2 \le a \le 4$
C
$ - 2 \le a \le 0$
D
$a \le - 2\,\,{\rm{or}}\,\,a \ge 4$

✓

Answer

Correct option: B.

$ - 2 \le a \le 4$

b
(b) $\int_0^a {\,\,x\,dx \le a + 4} $

$ \Rightarrow \frac{{{a^2}}}{2} \le a + 4$

$ \Rightarrow {a^2} \le 2a + 8$

$ \Rightarrow {a^2} - 2a - 8 \le 0$

$ \Rightarrow (a - 4)(a + 2) \le 0$

$ \Rightarrow - 2 \le a \le 4$.

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