If-for-every-integer-n-n-n-1-f-x-dx-n-2-then-the-value-of-2-4-f-x-dx-

Question Number 54028 by qw last updated on 28/Jan/19

If for every integer n, \underset{n}{\int^{n + 1}} f (x) d x = n^{2},

then the value of \underset{- 2}{\int^{4}} f (x) d x =

Answered by tanmay.chaudhury50@gmail.com last updated on 28/Jan/19

\int_{- 2}^{4} f (x) d x

\int_{- 2}^{- 2 + 1} f (x) d x + \int_{- 1}^{- 1 + 1} f (x) d x + \int_{0}^{0 + 1} f (x) d x + \int_{1}^{1 + 1} f (x) d x + \int_{2}^{2 + 1} f (x) d x + \int_{3}^{3 + 1} f (x) d x

[{(- 2)}^{2} + {(- 1)}^{2} + {(0)}^{2} + {(1)}^{2} + {(2)}^{2} + {(3)}^{2}]

= 4 + 1 + 0 + 1 + 4 + 9

= 19