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The integral I=int(sin(x^(2))+2x^(2)cos(...

The integral `I=int(sin(x^(2))+2x^(2)cos(x^(2)))dx` (where `=xh(x)+c`, C is the constant of integration). If the range of `H(x)` is `[a, b],` then the value of `a+2b` is equal to

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Knowledge Check

  • The integral I=int[xe^(x^(2))(sinx^(2)+cosx^(2))]dx =f(x)+c , (where, c is the constant of integration). Then, f(x) can be

    A
    `e^(x)sin(x^(2))`
    B
    `e^(x^(2))sin(x)`
    C
    `e^(x^(2))((x^(2))/(2))`
    D
    `(1)/(2)e^(x^(2))sin(x^(2))`

  • int("sin"(5x)/(2))/("sin"(x)/(2))dx is equal to (where, C is a constant of integration)

    A
    `2x + "sin" x + 2 "sin" 2x + C`
    B
    `x + 2"sin" x + 2 "sin" 2x + C`
    C
    `x + 2"sin" x + "sin" 2x + C`
    D
    `2x + "sin" x + "sin" 2x + C`

  • The integral int(1)/((1+sqrt(x))sqrt(x-x^(2)))dx is equal to (where C is the constant of integration)

    A
    `-2sqrt((1+sqrt(x))/(1-sqrt(x)))+C`
    B
    `-2sqrt((1-sqrt(x))/(1+sqrt(x)))+C`
    C
    `-sqrt((1+sqrt(x))/(1+sqrt(x)))+C`
    D
    `2sqrt((1+sqrt(x))/(1-sqrt(x)))+C`

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