Definite Integration Question 162
Question: The area bounded by the curve $ y=x{{(3-x)}^{2}} $ , the x-axis and the ordinates of the maximum and minimum points of the curve, is given by
Options:
A) 1 sq. unit
B) 2 sq. unit
C) 4 sq. unit
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Clearly, the curve $ y=x{{(3-x)}^{2}} $ has maximum at $ x=1 $ and minimum at $ x=3 $ .
$ \therefore $ Req. area $ =\int_1^{3}{x{{(3-x)}^{2}}dx} $
$ =\int_1^{3}{(x^{3}-6x^{2}+9x)dx} $
$ =[ \frac{x^{4}}{4}-2x^{3}+\frac{9x^{2}}{2} ]_1^{3}=4 $ sq. unit.
BETA
