# Find the Area Under the Curve y=1/x , [5,12]

,
Substitute for into then solve for .
Replace with in the equation.
Solve the equation for .
Rewrite the equation as .
Find the LCD of the terms in the equation.
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Since contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Multiply each term by and simplify.
Multiply each term in by in order to remove all the denominators from the equation.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Since , there are no solutions.
No solution
No solution
No solution
The area of the region between the curves is defined as the integral of the upper curve minus the integral of the lower curve over each region. The regions are determined by the intersection points of the curves. This can be done algebraically or graphically.
Integrate to find the area between and .
Combine the integrals into a single integral.
Subtract from .
The integral of with respect to is .
Evaluate at and at .
Evaluate.
Use the quotient property of logarithms, .
The absolute value is the distance between a number and zero. The distance between and is .
The absolute value is the distance between a number and zero. The distance between and is .
Find the Area Under the Curve y=1/x , [5,12]