`int_(-2)^(2)[x^(2)]dx=A+2B+sqrt(2)C`, तब
C का मान ज्ञात कीजिए ।

Options

A. `2`
B. `-2`
C. `(1)/(2)`
D. इनमें से कोई नहीं

Answer

B

Explanation

`int_(-2)^(2)[x^(2)]dx=2int_(0)^(2)[x^(2)]dx`
`[becausef(x)=[x^(2)]` एक सम फलन है ]
`=2[int_(0)^(1)[x^(2)]dx+int_(1)^(sqrt(2))[x^(2)]dx+int_(sqrt(2))^(sqrt(3))[x^(2)]dx+int_(sqrt(3))^(2)[x^(2)]dx]`
`[{:(because[x^(2)]=,):}{{:(0",",0le,xlt,1),(1",",1le,xlt,sqrt(2)),(2",",sqrt(2)le,xlt,sqrt(3)),(3",",sqrt(3)le,xlt,2):}]`
`=2[int_(0)^(1)0dx+int_(1)^(sqrt(2))1dx+int_(sqrt(2))^(sqrt(3))2dx+int_(sqrt(3))^(2)3dx]`
`=2[x]_(1)^(sqrt(2))+4[x]_(sqrt(2))^(sqrt(3))+6[x]_(sqrt(3))^(2)`
`=(10-2sqrt(3)-2sqrt(2))=A+2B+sqrt(2)C`
C=-2