Lucas Function

dynamic_programming/lucas_function.py

@@ -0,0 +1,29 @@
+# Giving the output
+def lucas_func(n):
+    # PREDFINING THE VALUES
+    a = 2
+    b = 1
+
+    if n == 0:
+        return a
+
+    # GENERATING THE NUMBER
+    for i in range(2, n + 1):
+        c = a + b
+        a = b
+        b = c
+
+    return b
+
+
+# USER INPUT
+n = int(input("Enter the position n to find the nth Lucas Number: "))
+print(f"The {n}th Lucas Number is: {lucas_func(n)}")
+
+"""
+
+THE OUTPUT:-
+Enter the position n to find the nth Lucas Number: 6
+The 6th Lucas Number is: 18
+
+"""

final_lucas_function.py

@@ -0,0 +1,29 @@
+# Giving the output
+def lucas_func(n):
+    # PREDFINING THE VALUES
+    a = 2
+    b = 1
+
+    if n == 0:
+        return a
+
+    # GENERATING THE NUMBER
+    for _ in range(2, n + 1):
+        c = a + b
+        a = b
+        b = c
+
+    return b
+
+
+# USER INPUT
+n = int(input("Enter the position n to find the nth Lucas Number: "))
+print(f"The {n}th Lucas Number is: {lucas_func(n)}")
+
+"""
+
+THE OUTPUT:-
+Enter the position n to find the nth Lucas Number: 6
+The 6th Lucas Number is: 18
+
+"""

maths/area.py

@@ -4,6 +4,8 @@
 """
 
 from math import pi, sqrt, tan
+import numpy as np
+from scipy.integrate import quad
 
 
 def surface_area_cube(side_length: float) -> float:
@@ -264,6 +266,25 @@ def area_rectangle(length: float, width: float) -> float:
     return length * width
 
 
+def area_of_parabola(x,a,b,c):
+    """
+    Area under the parabola y = 1x² + 0x + 0 from x = 0 to x = 2 is 2.666666666666667
+    """
+ return a * x**2 + b * x + c
+
+ def area_under_parabola(a, b, c, x1, x2):
+     area, _ = quad(parabola, x1, x2, args=(a, b, c))
+     return area
+  #example usage
+  a = 1
+  b = 0
+  c = 0
+ x1 = 0
+ x2 = 2
+
+area = area_under_parabola(a, b, c, x1, x2)
+print(f"Area under the parabola y = {a}x² + {b}x + {c} from x = {x1} to x = {x2} is {area}")
+
 def area_square(side_length: float) -> float:
     """
     Calculate the area of a square.