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int(2)^(8)f(x)dx where f(x)={:{(3x+4",",...

`int_(2)^(8)f(x)dx` where `f(x)={:{(3x+4",",2lexle3),(x^(2)+4",",3lexle8):}`.

Answer

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Evaluate int_(1)^(4)f(x)dx , where f(x)={:{(2x+8",",1lexle2),(6x",",2lexle4):} .

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Knowledge Check

  • int(2^(8x+3))/(2^(4x+3))dx:

    A
    `(1)/(4)(2^(4x))/(log8)+c`
    B
    `(1)/(8)(2^(8x))/(log4)+c`
    C
    `(16^(x))/(log2)+c`
    D
    `((24)^(x))/(log24)+c`

  • The inverse of f(x)={(x,"if",x lt 1),(x^(2),"if",1lexle4),(8sqrt(x),"if",x gt4):} is

    A
    `f^(-1)(x)={(x,"if",x lt 1),(sqrt(x),"if",1lexle16),((x^(2))/64,"if",xgt16):}`
    B
    `f^(-1)(x)={(-x,"if",x lt 1),(sqrt(x),"if",1lexle16),((x^(2))/64,"if",xgt16):}`
    C
    `f^(-1)(x)={(x^(2),"if",x lt 1),(sqrt(x),"if",1lexle16),((x^(2))/64,"if",xgt16):}`
    D
    `f^(-1)(x)={(2x,"if",x lt 1),(sqrt(x),"if",1lexle16),((x^(2))/8,"if",xgt16):}`

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