Let a, b and c be non - zero real numbers such that ` int _(0)^(3) (3ax ^(2) + 2bx +c) dx = int _(1)^(3) (3ax^(2) + 2bx +c) dx` , then

Question

Let a, b and c be non - zero real numbers such that ` int _(0)^(3) (3ax ^(2) + 2bx +c) dx = int _(1)^(3) (3ax^(2) + 2bx +c) dx` , then

Let a, b and c be non - zero real numbers such that ` int _(0)^(3) (3ax ^(2) + 2bx +c) dx = int _(1)^(3) (3ax^(2) + 2bx +c) dx` , then
A. `a+b+c= 3`
B. `a+b+c=1`
C. `a+b+c=0`
D. `a+b+c=2`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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)dx`
`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`

4 views Answered 2023-02-05 15:29