indefinite integral
Not what you're looking for?
1. A quantity of gas with an initial volume of 1 cubic foot and a pressure of 500 pounds per square foot expands to a volume of 2 cubic feet. Find the work done by the gas. (Assume that the pressure is inversely proportional to the volume; that is, the gas obeys the ideal gas law such that PV = constant.)
2. Find the indefinite integral and check the result by differentiation:
7. Find
9. Find the partial fraction expansion: (not sure how to handle the exponent of 3 in the denominator.)
Purchase this Solution
Solution Summary
Find the indefinite integral and check the result by differentiation.
Solution Preview
3. A quantity of gas with an initial volume of 1 cubic foot and a pressure of 500 pounds per square foot expands to a volume of 2 cubic feet. Find the work done by the gas. (Assume that the pressure is inversely proportional to the volume; that is, the gas obeys the ideal gas law such that PV = constant.)
Here we will set up the ideal gas law as the equation where k is the constant. We find the value of the constant k using the initial values of P = 500 and V = 1. This gives a value of k = 500 making the function .
We then integrate this function with respect to V over the interval from V = 1 to V = 2. This gives the work done as
.
So, the work done is about 346.6 foot-pounds.
2. Find the indefinite integral ...
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.