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Let f(x) be a continous function such th...

Let `f(x)` be a continous function such that `int_(m)^(n+1) f(x) dx =n^(3),n in Z` Then , the value of `int_(-30^(3)f(x) dx` is

A

9

B

`-27`

C

`-9`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`underset(-3)overset(3)int f(x)underset(r=0)overset(-5)sumunderset(-3+r)overset(-3+r+1)int f(x)dx`
` rArr underset(-3)overset(3)int f(x)dxunderset(r=0)overset(-5)sum (-3+r)^(3) [ :. underset(n)overset(n+1)int f(x)dx=n^(3)]`
`underset(-3)overset(3)int f(x)dx=[ (-3)^(3)+(-2)^(3)+(-1)^(3)+0^(2)+1^(3)+2^(3)]=-27`
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