Question: a. Evaluate tan x sec 2 x dx using the substitution u = tan x. b. Evaluate tan x sec 2 x dx

a. Evaluate ∫ tan x sec2 x dx using the substitution u = tan x.

b. Evaluate ∫ tan x sec2 x dx using the substitution u = sec x.

c. Reconcile the results in parts (a) and (b).

Step by Step Solution

★★★★★

3.31 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a If u tan x then du sec x dx Substituting gives f u d... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus Early Transcendentals Questions!

Q:

a. Evaluate cot x csc 2 x dx using the substitution u = cot x. b. Evaluate cot x csc 2 x dx using the substitution u = csc x. c. Reconcile the results in parts (a) and (b).

Q:

a. Evaluate x ln x 2 dx using the substitution u = x 2 and evaluating ln u du. b. Evaluate x ln x 2 dx using integration by parts. c. Verify that your answers to parts (a) and (b) are consistent.

Q:

An integrand with trigonometric functions in the numerator and denominator can often be converted to a rational integrand using the substitution u = tan (x/2) or equivalently x = 2 tan -1 u. The...

Q:

8. (40 pts!) Evaluate tan x sec x dx a. by setting u = tan x b. by setting u = sec x sin c. use the fact that tan x sec x dx = cox cosx 1 /2 T S dx, sin x cos x - dx = d. Graph results of a., b. and...

Q:

Symbolic answers must be entered using notation similar to the examples given below. If you enter decimal numbers for questions that indicate that a symbolic answer is required, it will be marked as...

Q:

1. (06.08 MC) Evaluate x - cos x sin x dx. (1 point) O O O 1 Oo 2. (06.08 MC) Using the substitution u = Vx+2. [, xx+2 dx is equal to which of the following? (1 point) O 2 /2 ( 4 4 - 24 2 ) du O 2 /...

Q:

a. Evaluate 2 tan x sec * x dx using the substitution u = tan x. b. Evaluate - tan x sec * x dx using the substitution u = sec x. c. Reconcile the results in parts (a) and (b). a. Rewrite the given...

Q:

a. Evaluate 2 tan x sec * x dx using the substitution u = tan x. b. Evaluate - tan x sec * x dx using the substitution u = sec x. c. Reconcile the results in parts (a) and (b). a. Rewrite the given...

Q:

Please #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 \f21. tan x sec x dx 22 . tan'0 sec*0 de 61. If "/4 tan'x sec x dx = I, express the value of of* tan'x sec x dx in terms of 1. 23. tan x...

Q:

Please #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 \f21. tan x sec x dx 22 . tan'0 sec*0 de 61. If "/4 tan'x sec x dx = I, express the value of of* tan'x sec x dx in terms of 1. 23. tan x...

Q:

Consider an asset with a current market value of $300,000 and a duration of 3.8 years. Assume the asset is partially funded through zero-coupon bonds which currently sells for $250,000 and has a...

Q:

Compute the partial derivatives of the CES function (exercise 2.35) f(x) = (a,x + azx +... + a,x)P. P+0

Q:

Georgina has $ 1 9 5 , 0 0 0 in her retirement account. She will not make any additional contributions, but her account will earn interest at j 1 2 = 6 % until she retires in three years. If she...

Q:

1. What problems GCL is facing? What are strengths and weakness of GCL? What external threats the company is facing? Do you think the credit requirements of the GCL are justified?

Q:

Determine whether the series is convergent or divergent. If it is convergent, find its sum. 1 1 + n=1

Q:

Test the series for convergence or divergence. 1 n=1 n + n cos'n

Q:

Use the sum of the first 10 terms to approximate the sum of the series Use Exercise 42 to estimate the error. Data From Exercise 42: Let a n be a series with positive terms and let r n = a n+1 /a n ....

Q:

(Time allowance estimation: 7 minutes) You have won a swepstake that gives you 12 annual installments of $25,000 with the first one to be received one year from today. If the annual discounting rate...

Q:

Shares A and B have the following returns: Stock A Stock B 1 0.09 0.05 2 0.07 0.03 3 0.13 0.04 4 0.02 0.01 5 0.07 0.02 a. What are the expected returns of the two shares? b. What are the standard...

Q:

o se that the citizens of Smalltown rank alternatives W,X,Y and Z as shown in the table from best a) What is Smalltown's raun. g over each pair of alternatives if we use the "method of majority...