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If int0^3 (3ax^2+2bx+c)dx=int1^3 (3ax^2+...

If `int_0^3 (3ax^2+2bx+c)dx=int_1^3 (3ax^2+2bx+c)dx` where `a,b,c` are constants then `a+b+c=`

A

`a+b+c=3`

B

`a+b+c=1`

C

`a+b+c=0`

D

`a+b+c=2`

Text Solution

Verified by Experts

The correct Answer is:
C
`int_(0)^(3)(3ax^(2)+2bx+c)dx=int_(1)^(3)(3ax^(2)+2bx+c)dx`
`rArr" "int_(0)^(1)(3ax^(2)+2bx+c)dx+int_(1)^(3)(3ax^(2)+2bx+c)dx`
`" "=int_(1)^(3)(3ax^(2)+2bx+c)`
`rArr" "int_(0)^(1)(3ax^(2)+2bx+c)dx=0`
`rArr" "[(3ax^(3))/(3)+(2bx^(2))/(2)+cx]_(0)^(1)=0`
`rArr" "a+b+c=0`
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