Approximate $\int _ { 0 } ^ { 1 } x ^ { 4 }$

question 24

Short Answer

Approximate $\int _ { 0 } ^ { 1 } x ^ { 4 }$ dx; n = 4, by (a) Simpson's rule and (b) the trapezoidal rule.
Enter your answers in that order as just unlabeled real numbers rounded to two decimal places, separated by a comma.

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Definitions:

Diametral Pitch

A measure of tooth density in gear sets, representing the number of teeth per unit of pitch diameter.

Circular Pitch

In gear design, the distance measured along the pitch circle between corresponding points on adjacent teeth.

Root Diameter

The diameter of a gear or screw measured at the base of the teeth or threads, where the material is the thickest.

Bevel Gears

Gears with intersecting shafts and conically shaped teeth that are used to change the axis of rotation in machinery.