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int(1)^(2)x^(2)dx is equal to...

`int_(1)^(2)x^(2)dx` is equal to

A

`lim_(nto oo) 1/n sum_(r=1)^(n)f(r/n)`

B

`lim_(nto oo) 1/n sum_(r=n+1)^(2n) f(r/n)`

C

`lim_(nto oo) 1/n sum_(r=1)^(n)f((r+n)/n)`

D

`lim_(nto oo) 1/n sum_(r=1)^(2n)f(r/n)`

Text Solution

Verified by Experts

The correct Answer is:
B, C
`lim_(nto oo) 1/n sum_(r=n+1)^(2n)f(r/n)=int_(1)^(2) f(x)dx`
`lim_(nto oo) 1/n sum_(r=1)^(n)f((r+n)/n)=int_(0)^(1)f(1+x)dx=int_(1)^(2)dx=int_(1)^(2)f(t)dt=int_(1)^(2)f(x)dx`
`lim_(nto oo) 1/n sum_(r=1)^(n)f(r/n)=int_(0)^(1)f(x)dx`
`lim_(n to oo) 1/n sum_(r=1)^(2n) f(r/n)=int_(0)^(2)f(x)dx`
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Knowledge Check

  • int_(1)^(2)(dx)/(x^(2)) is equal to

    A
    `1/2`
    B
    1
    C
    2
    D
    `-1`

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