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Numerade Educator

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Problem 81 Hard Difficulty

Show that $$ 0 \le \int^{10}_5 \frac{x^2}{x^4 + x^2 + 1} \, dx \le 0.1 $$ by comparing the integrand to a simpler function.

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0.1

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Video Transcript

Okay. What we know is that we have integral from 5 to 10 0 DX and we know that this is less than the subsequent and into roles. I escorted her extra fourth plus X squared, plus one on one over X scored as given in the problem. What this tells us now is that this as well as Thean Tre from five to 10 1 over X Cordy ax. If we plug this end, we end up with one tent. We know that zero is indeed less than or equal to the integral from 5 to 10 ex court over axe to the fourth plus x squared, plus one which is less than or equal to 0.1.