A) 1
B) 3
C) -1
D) 4
Correct Answer: A
Solution :
[a] (1) For \[c<1,\int_{c}^{1}{(8{{x}^{2}}-{{x}^{5}})dx=\frac{16}{3}}\] \[\Rightarrow \frac{8}{3}-\frac{1}{6}-\frac{8{{c}^{3}}}{3}+\frac{{{c}^{6}}}{6}=\frac{16}{3}\] \[\Rightarrow {{c}^{3}}\left[ -\frac{8}{3}+\frac{{{c}^{3}}}{6} \right]=\frac{17}{6}\]. Again, for \[c\ge 1,\] none of the values of c satisfy the required condition that \[\int_{1}^{c}{(8{{x}^{2}}-{{x}^{5}})dx=\frac{16}{3}\Rightarrow c+2=1}\].
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