Reference no: EM131109314
1. Choose TWO of the integrals below and evaluate on the next page(s).
1. ∫ln(x) dx
2. ∫1/(1 + 4x2)dx
3. ∫cos(x)e5xdx
4. ∫cos2 x dx
5. ∫6y 1.5 + sec2(y) + 7 dy
6. ∫cos2(x) sin3(x) dx
7. ∫te-tdt
8. ∫x/√(1 - x2)dx
9. ∫x sec2 x dx
10. ∫x/(x + 23)dx
2. Consider the region bounded by the curve y = 2x2 - x3 and x-axis on [0, 2]. Determine the volume of the solid obtained when this region is rotated about the y-axis.
3. Assume that the formula
∫(ln x)n dx = x (ln x)n - n∫(ln x)n-1dx (1)
is true for all positive integers n.
(a) Use equation (1) to compute ∫o1(ln x)2dx.
HINT: This means set n = 2.
(b) Use equation (1) to compute
∫o1(ln x)3dx.
HINT: This means set n = 3.
(c) Make a conjecture on the value of ∫o1(ln x)ndx.
4. You have just accepted a position with the Department of Defense working on ballistics. Your first assignment is as follows: Consider the region R bounded by the curve y = √(4 - x2) for 0 ≤ x ≤ 1, the line y = 0, and the line x = 0. Determine the surface area of the solid obtained by revolving R about the x axis.
5. (a) Compute the integral ∫oTxe-xdx
where T > 0.
(b) Compute limT→∞ ∫oTxe-xdx
|
Every mole of hydrogen gas
: How many moles of hydrochloric acid were added to the flask? The molar mass of hydrochloric acid is 36.3094 g/mol. Remember that the 6 M HCl solution was diluted by half with water. (molar mass = mass/moles) Choose the closest answer.A. 0.03 ..
|
|
An organizational structure for the it department
: Propose an organizational structure for the IT department that you feel would support the transformation of AgCredit into a processcentric organization
|
|
Explain the connection between nutrition and disease
: Explain the connection between nutrition and disease. Be sure to include information on chronic diseases, as well as malnutrition and other leading causes of death.
|
|
Give the response of each questions
: 1. What are the two basic sources of funds for all businesses?
|
|
Determine the surface area of the solid obtained
: Consider the region bounded by the curve y = 2x2 - x3 and x-axis on [0, 2]. Determine the volume of the solid obtained when this region is rotated about the y-axis.
|
|
Final temperature of both substances
: A 32.5-g cube of aluminum initially at 45.8 degree C is submerged in 105.3-g of water at 15.4 degree C. What is the final temperature of both substances at thermal equilibrium? (Assume that the aluminum and the water are thermally isolated from e..
|
|
Compute shins minimum amortization of the actuarial loss
: Shin Corporation had a projected benefit obligation of $3,100,000 and plan assets of $3,300,000 at January 1, 2010. Shin also had a net actuarial loss of $465,000 in accumulated OCI at January 1, 2010.
|
|
Describe the amount of long term and short term financing
: Describe the amount of long-term and short-term financing used to meet the total funds requirement under (1) an aggressive funding strategy and (2) a conservative funding strategy. Assume that, under the aggressive strategy, long term funds finance p..
|
|
The decision tree inductive learning algorithm
: The Decision Tree inductive learning algorithm may be used to generate "IF ... THEN" rules that are consistent with a set of given examples. Consider an example where 10 binary input variables X1, X2, , X10 are used to classify a binary output variab..
|