diff options
Diffstat (limited to '260/CH11/EX11.7/11_7.sce')
| -rw-r--r-- | 260/CH11/EX11.7/11_7.sce | 32 |
1 files changed, 32 insertions, 0 deletions
diff --git a/260/CH11/EX11.7/11_7.sce b/260/CH11/EX11.7/11_7.sce new file mode 100644 index 000000000..ae7d02fff --- /dev/null +++ b/260/CH11/EX11.7/11_7.sce @@ -0,0 +1,32 @@ +//Eg-11.7
+//pg-482
+
+clear
+clc
+
+//The function is to be integrated over the interval 0 to 1 using single and double segment applications of the trapezoidal rule.
+
+b = 1;
+a = 0;
+
+//The integration formula for single segment application of trapezoidal rule is I = (b-a)/2 * [f(a)+f(b)]
+
+I1 = (b-a)/2 * (exp(1) + exp(0));
+
+//The integration formula for double-segment application of trapezoidal rule is I = (b-a)/2n * [f(a)+2*f(a+h)+f(b)]
+
+n = 2;
+h = (b-a)/(n);
+
+I2 = (h/2)*(exp(0) + 2*exp(0+h) + exp(1));
+
+printf('The value of the integral using 1 segment is %f\n',I1)
+printf(' The value of the integral using 2 segments is %f\n',I2')
+
+//Using equation [28] we obtain the improved estimate as I = 4/3*I2 - 1/3*I1
+
+I = 4/3*I2 - 1/3*I1;
+
+printf(' Using equation [28] we obtain the improved estimate as I = %f\n\n',I)
+
+printf(' This value represents a much better estimate of the integral. Infact,\n it is closer to the exact value of the integral, 1.7183, than any of \n the values obtained using the trapezoidal rule above.\n')
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