A) \[\frac{7}{2}\]
B) \[\frac{13}{6}\]
C) \[\frac{17}{6}\]
D) \[\frac{19}{6}\]
Correct Answer: D
Solution :
\[A=\{(x,y)|y\ge {{x}^{2}}-5x+4,x+y\ge 1,y\le 0\}\] Here \[y\ge {{x}^{2}}-5x+4,x+y\ge 1,y\le 0\] Required area \[=\frac{1}{2}.22+\int\limits_{3}^{4}{(5x-{{x}^{2}}-4)dx}\] \[=2+\left[ \frac{5{{x}^{2}}}{2}-\frac{{{x}^{3}}}{3}-4x \right]_{3}^{4}\] \[=2+\frac{5}{2}(16-9)-\frac{1}{3}(64-27)-4(4-3)\] \[-2+\frac{35}{2}-\frac{37}{3}-4=\frac{19}{6}\]You need to login to perform this action.
You will be redirected in
3 sec