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How to Calculate Integral of Natural Logs

In calculus, the integral of a function allows you to compute the exact area underneath a curve. For a function f(x) over the interval from a to b, the area under the curve is F(b) - F(a), where the function F(x) is the integral of f(x). This formula is called the Second Fundamental Theorem of Calculus. In particular, if f(x) = Ln(x), the natural logarithm of x, then the integral function is F(x) = x*Ln(x) - x. You can use this equation to compute the area of a region under the curve of Ln(x).

Calculator

Instructions

- 1
  Assign the variables a and b to the endpoints of the interval so that a is the smaller number and b is the larger number. For example, if you compute the area under Ln(x) from 3 to 5, a = 3 and b = 5.
- 2
  Evaluate b*Ln(b) - b on your calculator and call this number B. For instance, if b = 5, then B = 3.0472, since 5*Ln(5) - 5 = 3.0472.
- 3
  Evaluate a*Ln(a) - a on your calculator and call this number A. If a = 3, then A = 0.2958, since 3*Ln(3) - 3 = 0.2958.
- 4
  Subtract A from B to compute the area. For example, since 3.0472 - 0.2958 = 2.7514, the area under the natural log curve between 3 and 5 is equal to 2.7514.

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