# Compute the Value of ∫ π 2 0 √ Sin X + Cos X D X Using Simpson’S (1/3)Rd Rule by Dividing into Six Subintervals. - Applied Mathematics 2

Sum

Compute the value of int_0^(pi/2) sqrt(sinx+cosx) dx using Simpson’s (1/3)rd rule by dividing into six Subintervals.

#### Solution

Let I = int_0^(pi/2) sqrt(sinx+cosx) dx

Dividing limits into 6 subintervals . n=6

a = 0, b=pi/2    thereforeh=(b-a)/n=pi/12

 x_0=0 x_1=pi/12 x_2=(2pi)/12 x_3=(3pi)/12 x_4=(4pi)/12 x_5=(5pi)/12 x_6=(6pi)/12 y_0=1 y_1=1.1067 y_2=1.1688 y_3=1.1892 y_4=1.1688 y_5=1.1067 y_6=1

Simpson’s (𝟏/𝟑)𝒓𝒅 rule :

"I"=h/3[X+2E+40]  -----------------(1)

𝑿=𝒔𝒖𝒎 𝒐𝒇 𝒆𝒙𝒕𝒓𝒆𝒎𝒆 𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆𝒔=𝒚𝟎+𝒚𝟔=𝟏+𝟏=𝟐
𝑬=𝒔𝒖𝒎 𝒐𝒇 𝒆𝒗𝒆𝒏 𝒃𝒂𝒔𝒆 𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆𝒔= 𝒚𝟐+𝒚𝟒=𝟐.𝟑𝟑𝟕𝟔
𝑶=𝒔𝒖𝒎 𝒐𝒇 𝒐𝒅𝒅 𝒃𝒂𝒔𝒆 𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆𝒔= 𝒚𝟏+𝒚𝟑+𝒚𝟒=𝟑.𝟒𝟎𝟐𝟔

"I"=pi/(3xx12)(2+2xx2.3376+4xx3.4026)……………….(from 1)

I = 1.7693

Concept: Numerical Integration‐ by Simpson’S 1/3rd
Is there an error in this question or solution?
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}