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int(sqrt2//3)^(sqrt3//3)(dx)/(sqrt(4-9x^...

`int_(sqrt2//3)^(sqrt3//3)(dx)/(sqrt(4-9x^(2)))=(pi)/(36)`
II `int_(-1)^(1)(1)/((1+x^(2))^(2))dx=(pi)/(4)+(1)/(2)`

A

only I is true

B

only II is true

C

both I and II are true

D

neither I nor true

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int_(sqrt2//3)^(sqrt(3)/3)(dx)/(sqrt(4-9x^(2)))=

int_(1//2)^(1)(1)/(sqrt(1-x^(2)))dx=

Knowledge Check

  • int (1)/(sqrt(4-9x^(2))dx=

    A
    `(1)/(2)Sin^(-1) ((3x)/(2))+c`
    B
    `(1)/(3)Cash^(-1) ((3x)/(5))+c`
    C
    `(1)/(3)Sin^(-1) ((3x)/(2))+c`
    D
    `(2)/(3)Sin^(-1) ((3x)/(2))+c`
  • int_(1//2)^(1) (1)/(sqrt(x-x^(2)))dx=

    A
    `pi`
    B
    0
    C
    `pi/4`
    D
    `pi/2`
  • int (1)/((1x^(2))sqrt(1-x^(2)))dx

    A
    `-(1)/(sqrt(2))Tanh^(-1)((sqrt(1+x^(2)))/(sqrt(2)x))+c`
    B
    `(1)/(sqrt(2))Tanh^(-1)((sqrt(1+x^(2)))/(sqrt(2)x))+c`
    C
    `-(1)/(sqrt(2))Tanh^(-1)((sqrt(1-x^(2)))/(sqrt(2)x))+c`
    D
    none
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