Question

$\left( \int _ { 0 } ^ { a } x d x \right) \leq ( a + 4 )$ then

• A. $0 \leq a \leq 4$
• B. $- 2 \leq a \leq 4$
• C. $- 2 \leq a \leq 0$
• D. $a \leq - 2$ or $a \geq 4$

Answer 1

Answer: (B)

$- 2 \leq a \leq 4$

Answer 2

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

$\Rightarrow a ^ { 2 } \leq 2 a + 8$ $\Rightarrow a ^ { 2 } - 2 a - 8 \leq 0$

$\Rightarrow ( a - 4 ) ( a + 2 ) \leq 0$ $\Rightarrow - 2 \leq a \leq 4$.