Definite Integration Question 156
Question: The value of c + 2 for which the area of the figure bounded by the curve $ y=8x^{2}-x^{5} $ , the straight lines $ x=1 $ and $ x=c $ and x-axis is equal to $ \frac{16}{3}, $ is
Options:
1
3
-1
4
Show Answer
Answer:
Correct Answer: A
Solution:
[a] (1) For $ c<1,\int_c^{1}{(8x^{2}-x^{5})dx=\frac{16}{3}-\left(\frac{8c^{3}}{3}-\frac{c^{6}}{6}\right)} $
$ \Rightarrow \frac{8}{3}-\frac{1}{6}-\frac{8c^{3}}{3}+\frac{c^{6}}{6}=\frac{16}{3} $
$ \Rightarrow c^{3}[ -\frac{8}{3}+\frac{c^{3}}{6} ]=\frac{17}{6} $ .
Again, for $ c\ge 1, $ none of the values of c satisfy the required condition that $ \int_1^{c}{(8x^{2}-x^{5})dx=\frac{16}{3}\Rightarrow c= -1} $ .
BETA
