?(a) Show that $1 \leqslant \sqrt{1+x^{3}} \leqslant 1+x^{3}$ for \(x \geqslant

Chapter 4, Problem 89

(choose chapter or problem)

(a) Show that $1 \leqslant \sqrt{1+x^{3}} \leqslant 1+x^{3}$ for $x \geqslant 0$.

(b) Show that $1 \leqslant \int_{0}^{1} \sqrt{1+x^{3}} d x \leqslant 1.25$.

Equation Transcription:

$1$ ⩽ $\sqrt{1\ \ +\ {x}^{3}}\$ ⩽ $1\ +\ {x}^{3}$ for $x$ ⩾ 0.

$1$ ⩽ $\int\limits_{0}^{1}\ \sqrt{1\ \ +\ {x}^{3}}\ \ \ dx$ ⩽ $1.25.$

Text Transcription:

1 leqslant sqrt{1+x^{3}} leqslant 1+x^{3} for x geqslant 0

1 leqslant int_{0}^{1} \sqrt{1+x^{3}} d x leqslant 1.25

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?(a) Show that \(1 \leqslant \sqrt{1+x^{3}} \leqslant 1+x^{3}\) for \(x \geqslant