A) 16
B) 14
C) 19
D) None of these
Correct Answer: C
Solution :
Given, \[\int_{n}^{n+1}{f(x)dx}={{n}^{2}}\] On putting \[n=-2,-1,0,1,2,3,\]we get \[\int_{-2}^{-1}{f(x)}\,dx=4\int_{-1}^{0}{f(x)}\,dx=1\] \[\int_{0}^{1}{f(x)}\,dx=0\int_{1}^{2}{f(x)}\,dx=1\] \[\int_{2}^{3}{f(x)}\,dx=4\int_{3}^{4}{f(x)}\,dx=9\] \[\therefore \] \[\int_{-2}^{4}{f(x)}\,dx=4+1+0+1+4+9=19\]You need to login to perform this action.
You will be redirected in
3 sec