# Definite Integrals Questions and Answers

Calculus

Definite Integrals Solutions

1. Evaluate the iterated integral: 3 √9-x^2 ∫ ∫ (x² + y²)dy dx 0 -√9-x^2

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

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

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

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

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 -

Calculus

Definite Integrals Solutions

= Sketch the region enclosed by y = 7x and y 6x2. Find the area of the region.

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

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? -

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

Calculus

Definite Integrals Solutions

The Lorenz curve for a country is given by y = 25.415. Calculate the country's Gini Coefficient.

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