Problem 6

README.md

@@ -274,3 +274,55 @@ legend('data','linear','pchip','spline')
 
 Plot
 ![](assets/README-93e4eb4a.png)
+
+# Problem 6
+
+Analytical Solution
+
+```
+fun = @(x) (1/6).*(x).^3+(1/2).*(x).^2+(x);
+q = integral(fun,2,3)
+```
+
+Gaussian Method
+
+```
+%1-Pt
+x = [0];
+a = [2];
+b = 2;
+c = 3;
+tildec = (c-b)/2*a;
+tildex = (c-b)/2*x + (c+b)/2;
+f = (1/6).*(tildex).^3+(1/2).*(tildex).^2+(tildex);
+value1 = sum(tildec.*f)
+
+%2-Pt
+x = [-0.57735,0.57735];
+a = [1,1];
+b = 2;
+c = 3;
+tildec = (c-b)/2*a;
+tildex = (c-b)/2*x + (c+b)/2;
+f = (1/6).*(tildex).^3+(1/2).*(tildex).^2+(tildex);
+value2 = sum(tildec.*f)
+
+
+%3-Pt
+x = [-0.77459666,0,0.77459666];
+a = [0.5555555,0.88888888,0.55555555];
+b = 2;
+c = 3;
+tildec = (c-b)/2*a;
+tildex = (c-b)/2*x + (c+b)/2;
+f = (1/6).*(tildex).^3+(1/2).*(tildex).^2+(tildex);
+value3 = sum(tildec.*f)
+```
+
+Outputs
+| Method | Value | Error |
+| ------------- | ------------- |-------------|
+| Analytical | 8.375 | 0% |
+| Gaussian 1-Pt  | 8.2292  | 1% |
+| Gaussian 2-Pt  | 8.375 | 0% |
+| Gaussian 3-Pt  | 8.375 | 0% |

analyticalprob6.m

@@ -0,0 +1,2 @@
+fun = @(x) (1/6).*(x).^3+(1/2).*(x).^2+(x);
+q = integral(fun,2,3)

gaussianprob6.m

@@ -0,0 +1,30 @@
+%1-Pt
+x = [0];
+a = [2];
+b = 2;
+c = 3;
+tildec = (c-b)/2*a;
+tildex = (c-b)/2*x + (c+b)/2;
+f = (1/6).*(tildex).^3+(1/2).*(tildex).^2+(tildex);
+value1 = sum(tildec.*f)
+
+%2-Pt
+x = [-0.57735,0.57735];
+a = [1,1];
+b = 2;
+c = 3;
+tildec = (c-b)/2*a;
+tildex = (c-b)/2*x + (c+b)/2;
+f = (1/6).*(tildex).^3+(1/2).*(tildex).^2+(tildex);
+value2 = sum(tildec.*f)
+
+
+%3-Pt
+x = [-0.77459666,0,0.77459666];
+a = [0.5555555,0.88888888,0.55555555];
+b = 2;
+c = 3;
+tildec = (c-b)/2*a;
+tildex = (c-b)/2*x + (c+b)/2;
+f = (1/6).*(tildex).^3+(1/2).*(tildex).^2+(tildex);
+value3 = sum(tildec.*f)