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Use the midpoint rule with the given value of n to approximate the integral. (Round your answer to four decimal places.)

16
0
sin
x
dx, n = 4

Use The Midpoint Rule With The Given Value Of N To Approximate The Integral Round Your Answer To Four Decimal Places 16 0 Sin X Dx N 4 class=

Sagot :

LammettHashidn

Split up [0, 16] into 4 equally-spaced subintervals of length [tex]\frac{16-0}4=4[/tex],

[0, 16] = [0, 4] U [4, 8] U [8, 12] U [12, 16]

with midpoints 2, 6, 10, and 14, respectively.

Then with the midpoint rule, we approximate the integral to be about

[tex]\displaystyle \int_0^{16} \sin(\sqrt x) \, dx \approx 4 \left(\sin(\sqrt2) + \sin(\sqrt6) + \sin(\sqrt{10}) + \sin(\sqrt{14})\right) \approx \boxed{4.1622}[/tex]

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