I'm a bit confused by the two integrals below. Why aren't they equal? What am I missing?

$\int_{-1}^2 \sqrt{t^2}\sqrt{9t^2+4} \,dt = 10,51$

$\int_{-1}^2 t\sqrt{9t^2+4} \,dt = 7,63$

  • 1
    $\begingroup$ You are assuming $\sqrt{t^2}=t$. $\endgroup$ – kimchi lover May 11 at 19:16
  • 3
    $\begingroup$ Because $t\ne\sqrt{t^2}$ in general. $\endgroup$ – Lord Shark the Unknown May 11 at 19:16
  • $\begingroup$ Always use : $\sqrt{t^2}=|t|$, to be correct and consistent. $\endgroup$ – Dr Zafar Ahmed DSc May 13 at 5:25

Since $$\sqrt{t^2}=|t|$$ they are not equal.


The integrand of the second integral is negative on $(-1,0)$, while the first is not.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.