Definite Integrals Questions and Answers

1. Evaluate the iterated integral: 3  √9-x^2 ∫   ∫
Calculus
Definite Integrals Solutions
1. Evaluate the iterated integral: 3 √9-x^2 ∫ ∫ (x² + y²)dy dx 0 -√9-x^2
The region bounded by the given curves is rotated about the
Calculus
Definite Integrals Solutions
The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. x = (y - 6)², x = 25; about y = 1
Use the method of cylindrical shells to find the volume
Calculus
Definite Integrals Solutions
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. x = 4y², y ≥ 0, x = 4; about y = 2
Use the method of cylindrical shells to find the volume
Calculus
Definite Integrals Solutions
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. 1/x y=0, x= 1, x = 2
Givenc (x is number of items) Demand function: (z) Supply
Calculus
Definite Integrals Solutions
Givenc (x is number of items) Demand function: (z) Supply function: a(z)=2./2 Find the equilibrium quantity: 2200 Find the consumers surplus at the equilibrium quantity: 9
Determine the volume of the solid generated by rotating
Calculus
Definite Integrals Solutions
Determine the volume of the solid generated by rotating function f(z) = [4,10]. 100 -z² about the x-axis on -
= Sketch the region enclosed by y = 7x and y 6x2. Find the
Calculus
Definite Integrals Solutions
= Sketch the region enclosed by y = 7x and y 6x2. Find the area of the region.
18 A company's marginal cost function is where x is the
Calculus
Definite Integrals Solutions
18 A company's marginal cost function is where x is the number of units. Find the total cost of the first 49 units (of increasing production from x=0 to x=49) Total cost: S
The traffic flow rate (cars per hour) across an intersection
Calculus
Definite Integrals Solutions
The traffic flow rate (cars per hour) across an intersection is r(t) 500+1000t 150t², where t is in hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 11 am? -
10. Consider the length of the graph of f(x) = == from (1,5)
Calculus
Definite Integrals Solutions
10. Consider the length of the graph of f(x) = == from (1,5) to (5,1). Approximate the length by finding the sum X of the lengths of 4 line segments, as shown in the following figure. Round your final
The Lorenz curve for a country is given by y = 25.415.
Calculus
Definite Integrals Solutions
The Lorenz curve for a country is given by y = 25.415. Calculate the country's Gini Coefficient.
A psychologist is studying the self image of smokers, as
Calculus
Definite Integrals Solutions
A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score, μ, for the population of all