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If f(x) = x^3 and F(x) = \int f(x)\;dx, then which of the following is the value of F'(x)?

  • Option 1)

    x^{3}

  • Option 2)

    x^{3} + 1

  • Option 3)

    x^{3} - 1

  • Option 4)

    Can be any of A, B, C

 

Answers (1)

best_answer

As we have learnt,

 

Reason for indefinite integration -

We know that   \frac{\mathrm{d} }{\mathrm{d} x}\left ( c \right )=0  , this implies that  F\left ( x \right )  and F\left ( x \right )+c  are both integrals of the same function f\left ( x \right ) . For different values of c, we obtain different integrals of f\left ( x \right ). So f\left ( x \right ) is not definite hence indefinite .

- wherein

Where   \frac{\mathrm{d}}{\mathrm{d}x}\left ( c \right ) is differential of constant w.r.to x

 

 \\*F(x) = \int f(x)dx = \int x^{3}dx = \frac{x^4}{4} + c \\* F'(x) = x^{3} + 0

 


Option 1)

x^{3}

Option 2)

x^{3} + 1

Option 3)

x^{3} - 1

Option 4)

Can be any of A, B, C

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prateek

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