(a) Using a trigonometricsubstitution, compute the integral and show that for a 0 (b) Verify the formula via differentiation dx 1 1 S (8 6) 26 ( x a tan x) C a...

a Let x a tan 0 Then dx a sec 0 de and 1 S S dx x a Since x a tan 8 we construct a right trian ...

(a) Using a trigonometricsubstitution, compute the integral and show that for a > 0 (b) Verify the...

Question:

(a) Using a trigonometricsubstitution, compute the integral and show that for a > 0

dx 1 S (x + 41 = 26 ( x +4 + = tan- x) + C 1 -

(b) Verify the formula via differentiation.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 01, 2023 08:03 AM

(a) Using a trigonometric substitution, compute the integral and show that for a > 0 (b) Verify the formula via differentiation. dx x + a S 1 - D tan - + C a
Write a complete Python program that computes some measurements related to a swimming pool. Our pool does not have a shallow end, the depth is the same along the length of the pool. From a diving...
5. Design a direct-mapped cache structure. The cache has the capacity of 8kB (kilo-byte), assuming 1 block is 512 bytes, and 1 valid bit, 1 tag bit. Calculate (S, E, B, m), draw and explain the cache...
The following are comparative financial statements of the Cohen Company for 2006, 2007, and 2008: Additional information: Credit sales were 65% of net sales in 2007 and 60% in 2008. At the beginning...
The following condensed income statements and balance sheets are available for Planter Stores for a two-year period. (All amounts are stated in thousands of dollars.) Before releasing the 2010 annual...
A turbine operates adiabatically with superheated steam entering at T1 and P1 with a mass flow rate m. The exhaust pressure is P2 and the turbine efficiency is . For OIK of the following sets of...
12. Assume the same bonds and numeraire as in the previous question. Suppose that P1/P3 is a martingale following a geometric Brownian process with annual standard deviation 1= 0.10, and that P2/P3...
Measuring the height of a California redwood tree is very difficult because these trees grow to heights over 300 feet. People familiar with these trees understand that the height of a California...
A project manager needs to understand the different costs that a project may incur. Making reference to a project of your choice, critically discuss the different types of project costs involved in...
Let I = dx/x 2 4x + 8. (a) Complete the square to show that x 2 4x + 8 = (x 2) 2 + 4. (b) Use the substitution u = x 2 to show that I =du/u 2 + 2 2 . Evaluate the u-integral. (c) Show that I = ln...
Compute r 0 1/(4 x 2 ) 3/2 dx, expressing the result in terms of r. Then, discuss what happens to the value of the definite integral as r approaches 2.
An airplane is flying at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over an observer on the ground. How fast is the...
What are major initiatives would you expect to see in a strategic plan focusing on a public health organization?
The purchase of $\$ 500$ of supplies on account will: a. Increase both assets and stockholders' equity by $\$ 500$ b. Increase assets and decrease liabilities by $\$ 500$ c. Increase assets and...
Venus Company owned a service truck that was purchased at the beginning of 2011 for $\$ 20,000$. It had an estimated life of three years and an estimated salvage value of $\$ 2,000$. Venus uses...
You are observing the sales department staff using exponential smoothing to fore- cast monthly sales. Their forecast for January's sales was 12,000 units. January's actual sales figure became...
Use the ID3 algorithm to build the full decision tree for the data set given in Section 10.9.2. 10.9.2 Example We will start with the training data given below: Film Country of origin Big star Genre...
The amount of improvement of a genetic disease is measured for 18 patients who are randomly assigned to the nine experimental configurations, with two patients to each configuration, corresponding to...
Reread the discussion leading to the result given in (7). Does the matrix sI - A always have an inverse? Discuss.
Express the given quantity as a single logarithm. ln 10 + 2 ln 5
Find the functions (a) f g, (b) gf, (c) ff, and (d) gg and their domains. f(x) = x/1 + x, g(x) = sin 2x
Graph several members of the family of functions where a > 0. How does the graph change when b changes? How does it change when a changes? f(x) 1 + aebr
Read the following and then answer the questions below:September 12: A Brisbane business offers by letter to sell 500 tyres to a New Zealand company. The Brisbane company does not specify a method of...
Fred returns home from work one day to discover his house surrounded by police. His wife is being held hostage and threatened by her captor. Fred pleads with the police to rescue her and offers...
Would like you to revisit one of these. Consideration must be clear and measurable.if you can't measure it then how can you show it has / has not been done?How can you sue someone for breach of...

(a) Using a trigonometricsubstitution, compute the integral and show that for a > 0 (b) Verify the...

Question:

dx 1 1 S (8² + 6²)² = 26² ( x² + a² + tan²-¹ x) + C - a

Step by Step Answer:

a Let x a tan 0 Then dx a sec 0 de and 1 S S dx x a Since x a tan 8 we construct a right trian...View the full answer

Calculus

Students also viewed these Mathematics questions