# Chapter 5 - The Integral - 5.2 The Definite Integral - Exercises - Page 246: 75

$$\int_{0}^{1} x^{5} d x \leq \int_{0}^{1} x^{4} d x$$ $$\int_{1}^{2} x^{4} d x \leq \int_{1}^{2} x^{5} d x$$

#### Work Step by Step

Since $x^{5} \leq x^{4},$ for $x\in [0,1]$, then $$\int_{0}^{1} x^{5} d x \leq \int_{0}^{1} x^{4} d x$$ and $x^{4} \leq x^{5}$ for $x \in[1,2]$, then $$\int_{1}^{2} x^{4} d x \leq \int_{1}^{2} x^{5} d x$$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.