Name: Calculus I — Math 161 Final Exam
... 2. (8 points) A cylindrical container with no top is to be constructed to hold 6000 cm3 of a liquid. Suppose that the cost of the material used for the bottom is 5 cents/cm2 , and the cost of the material used for the curved lateral side is 3 cents/cm2 . (a) Find an expression for the the cost of t ...
... 2. (8 points) A cylindrical container with no top is to be constructed to hold 6000 cm3 of a liquid. Suppose that the cost of the material used for the bottom is 5 cents/cm2 , and the cost of the material used for the curved lateral side is 3 cents/cm2 . (a) Find an expression for the the cost of t ...
MATH 1920 --- CALCULUS II COURSE SYLLABUS INSTRUCTOR
... 1. Interpret the area enclosed between curves as a definite integral and compute its value 2. Set up the Riemann sum representing the volume enclosed by a geometric solid, convert the result to a definite integral and compute its value. 3. Interpret a volume of revolution of a function’s graph aroun ...
... 1. Interpret the area enclosed between curves as a definite integral and compute its value 2. Set up the Riemann sum representing the volume enclosed by a geometric solid, convert the result to a definite integral and compute its value. 3. Interpret a volume of revolution of a function’s graph aroun ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.