Math Problem Statement

y = ln(x-1)와 y축 및 y = -1, y = 2로 둘러싸인 부분의 넓이는?

Solution

The problem is asking to calculate the area enclosed by the curve y=ln(x1)y = \ln(x-1), the yy-axis, and the horizontal lines y=1y = -1 and y=2y = 2.


Solution Outline:

  1. Understand the problem:
    • The curve is y=ln(x1)y = \ln(x-1), so ( x = e^y +

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Math Problem Analysis

Mathematical Concepts

Logarithmic Functions
Area Calculation
Integration

Formulas

y = ln(x-1)
Area between curves: A = ∫ from a to b of (f(x) - g(x)) dx

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12