A) \[\frac{24}{5}\pi \]
B) \[-2\le a\le 4\]
C) \[-2\le a\le 0\]
D) \[a\le -2\,\,\text{or}\,\,a\ge 4\]
Correct Answer: B
Solution :
\[\int_{0}^{a}{\,\,x\,dx\le a+4}\]\[\Rightarrow \frac{{{a}^{2}}}{2}\le a+4\] \[\Rightarrow {{a}^{2}}\le 2a+8\] \[\Rightarrow {{a}^{2}}-2a-8\le 0\] \[\Rightarrow (a-4)(a+2)\le 0\]\[\Rightarrow -2\le a\le 4\].
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