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Problem 65 Hard Difficulty

Use properties of integrals, together with Exercises 27 and 28, to prove the inequality.

$ \displaystyle \int^3_1 \sqrt{x^4 + 1} \,dx \ge \frac{26}{3} $


$\int_{1}^{3} \sqrt{x^{4}+1} \geq \frac{26}{3}$

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Video Transcript

okay. The comparison property of Integral says that the integral from 1 to 3 squirt of ex forth plus one, it's greater than or equal to the integral from 1 to 3 of X squared DX. Therefore, we now know the intro from 1 to 3 sort of X to the fourth plus one is greater than or equal to three cubed minus one cubed over three, which is 26 over three.