Find the Polynomial of Lowest Degree That Will Approximate $F ( x )$

question 426

Multiple Choice

Find the polynomial of lowest degree that will approximate $F ( x )$ throughout the given interval with an error of magnitude less than than $10 ^ { - 3 }$ .
- $$F ( x ) = \int _ { 0 } ^ { x } \sin ^ { 3 } d t , [ 0,1 ]$$

• A) \(x ^ { 3 } - \frac { x ^ { 9 } } { 6 }\)
• B) \(x ^ { 3 } - \frac { x ^ { 7 } } { 6 }\)
• C) \(\frac { x ^ { 4 } } { 4 } - \frac { x ^ { 10 } } { 60 }\)
• D) \(\frac { x ^ { 4 } } { 4 } - \frac { x ^ { 8 } } { 48 }\)

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