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How to solve this problem- - Integral Calculus - JEE Main-12

If f'(x)= 4x^{3}   and F(x)= \int f'(x)dx  

F(0) = 0 Find F(1)

  • Option 1)

    0

  • Option 2)

    -1

  • Option 3)

    1

  • Option 4)

    2

 
Answers (1)
92 Views
V Vakul

As we have learned

Rule for integration -

Integration of differential of a function is the function itself .

\int f{}'\left ( x \right )dx=f\left ( x \right )+c

 

- wherein

where    f{}'\left ( x \right )=\frac{\mathrm{d} }{\mathrm{d} x}\left \{ f(x) \right \}   

 

 988

F(x)= \int 4x^{3}dx= x^{4}+C

F(0)= C =\Rightarrow F(1)=1


Option 1)

0

This is incorrect

Option 2)

-1

This is incorrect

Option 3)

1

This is correct

Option 4)

2

This is incorrect

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