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

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

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

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    $\begingroup$ You are assuming $\sqrt{t^2}=t$. $\endgroup$ – kimchi lover May 11 at 19:16
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    $\begingroup$ 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
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Since $$\sqrt{t^2}=|t|$$ they are not equal.

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

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