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Why can I not use leibniz integral rule in this case?

0

$begingroup$

$int_0^x f(t)dt to 5 ~textas~ |x|to 1 $find number of integers in range of $p $ so that the equation $2x + int_0^x f(t)dt=p$ has two roots opposite signs in $(-1,1)$

Using leibniz rule on the given equation differentiating gives $$f(x)=-2$$ Therefore $$int_0^x f(t)dt to 5$$

becomes
$$-2x + c to 5$$

Which can not satisfy the condition uniquely for $|x|to 1$ gives two values of c for $^+ _- 1$

definite-integrals

share|cite|improve this question

edited Mar 30 at 23:01

Gerry Myerson

148k8152306

asked Mar 30 at 16:42

AvkaAvka

706

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  It’s ‘int_0^x’
  $endgroup$
  – Randall
  Mar 30 at 16:46
  

  
  
  
  

add a comment | 

0

$begingroup$

$int_0^x f(t)dt to 5 ~textas~ |x|to 1 $find number of integers in range of $p $ so that the equation $2x + int_0^x f(t)dt=p$ has two roots opposite signs in $(-1,1)$

Using leibniz rule on the given equation differentiating gives $$f(x)=-2$$ Therefore $$int_0^x f(t)dt to 5$$

becomes
$$-2x + c to 5$$

Which can not satisfy the condition uniquely for $|x|to 1$ gives two values of c for $^+ _- 1$

definite-integrals

share|cite|improve this question

edited Mar 30 at 23:01

Gerry Myerson

148k8152306

asked Mar 30 at 16:42

AvkaAvka

706

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  It’s ‘int_0^x’
  $endgroup$
  – Randall
  Mar 30 at 16:46
  

  
  
  
  

add a comment | 

$begingroup$

$int_0^x f(t)dt to 5 ~textas~ |x|to 1 $find number of integers in range of $p $ so that the equation $2x + int_0^x f(t)dt=p$ has two roots opposite signs in $(-1,1)$

Using leibniz rule on the given equation differentiating gives $$f(x)=-2$$ Therefore $$int_0^x f(t)dt to 5$$

becomes
$$-2x + c to 5$$

Which can not satisfy the condition uniquely for $|x|to 1$ gives two values of c for $^+ _- 1$

definite-integrals

share|cite|improve this question

edited Mar 30 at 23:01

Gerry Myerson

148k8152306

asked Mar 30 at 16:42

AvkaAvka

706

$endgroup$

share|cite|improve this question

edited Mar 30 at 23:01

Gerry Myerson

148k8152306

asked Mar 30 at 16:42

AvkaAvka

706

share|cite|improve this question

edited Mar 30 at 23:01

Gerry Myerson

148k8152306

asked Mar 30 at 16:42

AvkaAvka

706

edited Mar 30 at 23:01

Gerry Myerson

148k8152306

edited Mar 30 at 23:01

Gerry Myerson

148k8152306

asked Mar 30 at 16:42

AvkaAvka

706

asked Mar 30 at 16:42

AvkaAvka

706