1 files changed, 52 insertions, 0 deletions
diff --git a/tutorials/module_3/3_4_More_integral.md b/tutorials/module_3/3_4_More_integral.md
new file mode 100644
index 0000000..1e9c3c2
--- /dev/null
+++ b/tutorials/module_3/3_4_More_integral.md
@@ -0,0 +1,52 @@
+# More integral
+
+### Newton-Cotes Algorithms for Equations
+### Adaptive Quadrature
+
+
+## Problems 
+
+## Numerical Integration to Compute Work
+In physics we've learned that work is computed
+$$
+Work = force * distance
+$$
+This can be written in int's integral form:
+$$
+W = \int{F(x)dx}
+$$
+If F(x) is easy to integrate, we could solve this problem analytically. However, a realistic problem the force may not be available to you as a function, but rather, tabulated data. Suppose some measurements were take of when a weighted box was pulled with a wire. If we data of the force on the wire and the angle of the wire from the horizontal plane.
+
+| x (ft) | F(x) (lb) | θ (rad) | F(x) cos θ |
+| ------ | --------- | ------- | ---------- |
+| 0      | 0.0       | 0.50    | 0.0000     |
+| 5      | 9.0       | 1.40    | 1.5297     |
+| 10     | 13.0      | 0.75    | 9.5120     |
+| 15     | 14.0      | 0.90    | 8.7025     |
+| 20     | 10.5      | 1.30    | 2.8087     |
+| 25     | 12.0      | 1.48    | 1.0881     |
+| 30     | 5.0       | 1.50    | 0.3537     |
+|        |           |         |            |
+Use the trapezoidal rule to compute the work done on the box.
+
+## Implementing the Composite Trapezoidal Rule
+
+Implement a Python function to approximate integrals using the trapezoidal rule.
+
+```python
+import numpy as np
+
+def trapz(f, a, b, n):
+    x = np.linspace(a, b, n+1)
+    y = f(x)
+    h = (b - a) / n
+    return h * (0.5*y[0] + y[1:-1].sum() + 0.5*y[-1])
+
+# Example tests
+f1 = np.sin
+I_true1 = 2.0   # ∫_0^π sin(x) dx
+for n in [4, 8, 16, 32]:
+    print(n, trapz(f1, 0, np.pi, n))
+```
+
+Compare the results for increasing $n$ and observe how the error decreases with $O(h^2$).