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Numerade Educator

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Problem 55 Medium Difficulty

What is wrong with the equation?

$ \displaystyle \int^1_{-2} x^{-4} \, dx = \frac{x^{-3}}{-3} \Bigg]^1_{-2} = -\frac{3}{8} $

Answer

$f(x)=x^{-4}$ is not continuous on the interval $[-2,1],$ so $F T C 2$ cannot be applied. In fact, $f$ has an infinite discontinuity at $x=0,$ so $\int_{-2}^{1} x^{-4} d x$ does not exist.

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Video Transcript

okay. You know, we have the integral from negative to Tawan acts to the negative forth detox. And remember, when we integrate, we increase the exploited by one divide by the new X poona giving us negative three divided by eight. Now what we know is that this integral cannot be solved until we know later on what is wrong with one over X to the fourth. Because it's positive on its domain. So negative three eights doesn't really make sense. Because if we have positive values, the negative three is obviously negative. So what? This tells us that there's a discontinuous at X equals zero. There's Dace continuity.