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Enter the function, limits, and select the variables. The calculator will determine the area under the bell curve, providing detailed calculations.
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The Area Under the Curve (AUC) Calculator helps you evaluate definite integrals quickly and accurately. By entering a function and specifying upper and lower limits, you can compute the exact area under the curve along with detailed step-by-step integration.
In calculus, the area under a curve represents the definite integral of a function between two limits. If we have a function f(x) defined between x = a and x = b, the area is calculated as:
AUC = ∫ab f(x) dx
If the function lies above the x-axis, the integral is positive. If it lies below the x-axis, the integral becomes negative, but the geometric area is always considered positive.
AUC = ∫ab f(x) dx
Find the area under: f(x) = 6x + 3, from x = 0 to x = 4
Step 1: Set up the integral
∫04 (6x + 3) dx
Step 2: Integrate
Step 3: Antiderivative
F(x) = 3x² + 3x
Step 4: Apply limits
F(4) − F(0)
= (3·4² + 3·4)
= 60
Final Answer: AUC = 60
Find the area under: y = x³ + 5, from x = 0 to x = 1
∫01 (x³ + 5) dx
F(x) = x⁴/4 + 5x
F(1) − F(0) = 21/4
Final Answer: AUC = 21/4
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