Browse Questions

# $\int \limits_0^a x dx < a+4$ then

$\begin {array} {1 1} (a)\;0 \leq a \leq 4 \\ (b)\;a \leq -2\;or\; \geq 0 \geq 4 \\ (c)\;-2 \leq a \leq 0 \\ (d)\;-2 \leq a \leq 4 \end {array}$

Can you answer this question?

$\bigg[ \large\frac{x^2}{2}\bigg]_0^a $$< a+4 \large\frac{a^2}{2}$$ < a+4$
$a^2 < 2a+b$
$a^2 -2(1-b) <0$
$(a-4)(a+2) <0$
$a <-2,a <4$
Hence b is the correct answer.
answered Dec 17, 2013 by