The Area A of the region bounded by the curves y = f(x), y = g(x) and the lines x = a, x = b, where f and g are continuous f(x) >= g(x) for all x in [a, b] is
Find the area of the region bounded above by y = x2 + 1, bounded below by y = x, and bounded on the sides by x = 0 and x = 1.
The upper boundary curve is y = x2 + 1 and the lower boundary curve is y = x.
Using the formula,
Find the area between the two curves y = x2 and y = 2x – x2.
Step 1: Find the points of intersection of the two parabolas by solving the equations simultaneously.
x2 = 2x – x2
2x2 – 2x = 0
2x(x – 1) = 0
x = 0 or 1
The points of intersection are (0, 0) and (1, 1)
Step 2: Find the area between x = 0 and x = 1
Calculus - Finding the Area Under the Curve (1 of 7)
Find the area under the curve y = x2 from x = 0 to x = 4
The Area Under a Curve: approx. the definite integral.
Approximate the area under the curve f(x) = x2 from x = 1 to 3. Use n = 4 rectangles.
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