Question: Evaluate sin x cos x dx by four methods: (a) The substitution u = cos x, (b) The substitution u = sin x, (c) The

Evaluate ∫ sin x cos x dx by four methods:
(a) The substitution u = cos x,
(b) The substitution u = sin x,
(c) The identity sin 2x = 2 sin x cos x, and
(d) Integration by parts. Explain the different appearances of the answers.

Step by Step Solution

★★★★★

3.44 Rating (179 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Let u cos 2 Then du sin x dx f sin x cos x dx fudu u C cosx C b Let u sin z Then du co... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

M-C-I (236).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

sin u / 2 = - 1 - cos u / 2 When u is in the second quadrant.

Evaluate the integral. a. x cos 5x dx b. te-3t dt c. (x2 +2x) cos x dx

Evaluate the integral cot x csc2x dx by parts in two different ways. (a) By differentiating cot x (b) By differentiating csc x (c) Show that the two results are equivalent up to a constant.

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...

Evaluate sin x cos x dx using the given method. Explain how your answers differ for each method. (a) Substitution where u = sin x (b) Substitution where u = cos x (c) Integration by parts (d) Using...

Evaluate the following integral. 2 - 4x sin 3 (x2) dx O JC 4x sin 3 (x2) dx = (Type an integer or a simplified fraction.) OEvaluate 3 18 tan "x dx. 3 18 tan ~x dx =Evaluate the following integral. 6...

Evaluate the integral! 17 sin ?() cos 3 ( # ) ox Step 1 since 17 sin? (x) cos (x) dx has an odd power of of cos(x), we will convert all but one power to sines. We know that cos ( x) - 1 - 1 - sin = (...

Number 9 ONLY Preliminary Questions 1. Which of the following integrals is a candidate for the Substitution Method? (a ) ( 5x 4 sin (x5) dx (b) sin' x cos x dx (c) ( x5 sin x dx 2. Find an...

Lab 12: Substitution Rule Show all work on a separate sheet of paper with justifications where necessary. Answers should be clearly marked or boxed. Print first and last names of each group member at...

Let Î± and Î² be any two constants such that a The base of the rectangle has length Î² Î± and the height of the rectangle is 1/ ( Î²...

As shown in figure below, that give use the memory circuit of 8086 microprocessor, how will you replace the two NANDS gates in the circuit with one 3-to-8 decoder without changing the memory size or...

Provide an explanation of the following: Expenses: 1. Salaries and Wages: o Current Month: Actual spending is $7,317, which is $345 below the expected budget. o Year-to-Date: Costs amount to $66,068...

Kalin Corporation had 2010 net income of $1,000,000. During 2010, Kalin paid a dividend of $2 per share on 100,000 shares of preferred stock. During 2010, Kalin had outstanding 250,000 shares of...

A tracer is used to characterize the degree of mixing in a continuous stirred tank. Water enters and leaves the mixer at a rate of V (m 3 /min). Scale has built up on the inside walls of the tank, so...

A copper rod and an aluminum rod of the same length and cross-sectional area are attached end to end (Fig. 14-18). The copper end is placed in a furnace maintained at a constant temperature of 250oC....

Find the arbitrage opportunity (opportunities?). Assume for simplicity that coupons are paid annually. In each case the face value of the bond is $1,000. Price (S) Bond Coupon (S) Maturity (years)...

A jet fighter pilot knows he is able to withstand an acceleration of 9g before blacking out. The pilot points his plane vertically down while traveling at Mach 3 speed and intends to pull up in a...

Compute the average total cost, average variable cost, and marginal cost of producing 60 and 72 haircuts. Draw the graph of the three curves between 60 and 72 haircuts.

Find the area between a large loop and the enclosed small loop of the curve r = 1 + 2 cos 3.

Find all points of intersection of the given curves. r = sin , r = 1 - sin

Find all points of intersection of the given curves. r = cos 3, r = sin 3

12. Abbott Labs is 1.2, the expected return of Abbott Labs is: If the market risk premium is 7%, the risk free rate is 2%, and beta of the 9.4% b. 10.4% 11.4% d. 12.4% a. C. II. Chapter 12 (13...

A project that provides annual cash flows of $2,300 for nine years costs $9,500 today. Requirement 1: At a required return of 11 percent, what is the NPV of the project? (Do not round intermediate...

Green Planet Corporation has 6 , 4 0 0 shares of noncumulative 1 0 % preferred stock with a $ 2 par value and 2 1 , 4 0 0 shares of common stock with a $ 0 . 0 1 par value. During its first two years...