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Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of $ n $. (Round your answers to six decimal places.)

$ \displaystyle \int_0^4 x^3 \sin x\ dx $ , $ n = 8 $

a.$T_{8}=-7.276910$

b.$M_{8}=-4.818251$

c.$S_{8}=-5.605350$

Integration Techniques

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Missouri State University

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University of Wisconsin - Madison

Integration Techniques