Use Simpson’s Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer w

Question

Use Simpson’s Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by your calculator.

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Jezebel 3 years 2021-08-14T02:54:25+00:00 1 Answers 36 views 0

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  1. thienhuong
    0
    2021-08-14T02:56:00+00:00
    Reply

    Answer:

    The answer is “7.248934“.

    Step-by-step explanation:

    The area of the curve obtained after rotating it about the x-axis is
    :

    2 \pi \int^2_1 y \sqrt{1+ \{ \frac{dy}{dx}\}^2 \ dx}\\\\y=x\ \ln \ x \ And \ \frac{dy}{dx}=1+ \lh\ x

    So, The area of the curve obtained after rotating it about the x-axis is
    :
    2 \pi \int^2_1 (x \ln \ x) \sqrt{(\ln\ x)^2+ 2 \ln \ x+ 2\ dx}\\\\

    Simpson’s rule approximation with n=10 is:

    (\frac{1}{3})\times (0.1) \times ( f(1) + 4 \times f(1.1) + 2\times f(1.2) + 4 \times f(1.3) + 2 \times f(1.4) + 4 \times f(1.5) + 2 \times f(1.6) + 4 \times f(1.7) + 2 \times f(1.8) + 4 \times f(1.9) + f(2) ) = 7.248933= 7.248934  

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