Step 1: Solution-(1) Given: For R = [0,1] × [0,1] 2 I = √ √(xy)² cos(x³)dxdy R Our aim is to evaluate the given integral Step 2: Calculation: I = S√(xy)² cos(x³)dxdy R I = S₁₂ f₁ x² y² cos(x³) dxdy I = (f²x² cos(x³ ) d x) (f₁ y²dy) = Let x³ 3 t⇒ 3x² dx = dt f₁² fox² cos(x³) dx = cos(t)dt fox² cos(x³)dx = (sint) | So x² cos(x3)dx=(sin1 - sin0) Sox2 cos(x³)dx x² cos(x³)dx = (sin1 - 0) sin1 = 3 So y²dy = (5) 1 0 So y² dy = -0 = 1/3 Hence we get: I 3 = (sinl) (½³) = (sinl) 9

Step 1: Solution-(1) Given: For R = [0,1] × [0,1] 2 I = √ √(xy)² cos(x³)dxdy R Our aim is to evaluate the given integral Step 2: Calculation: I = S√(xy)² cos(x³)dxdy R I = S₁₂ f₁ x² y² cos(x³) dxdy I = (f²x² cos(x³ ) d x) (f₁ y²dy) = Let x³ 3 t⇒ 3x² dx = dt f₁² fox² cos(x³) dx = cos(t)dt fox² cos(x³)dx = (sint) | So x² cos(x3)dx=(sin1 - sin0) Sox2 cos(x³)dx x² cos(x³)dx = (sin1 - 0) sin1 = 3 So y²dy = (5) 1 0 So y² dy = -0 = 1/3 Hence we get: I 3 = (sinl) (½³) = (sinl) 9

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

See similar textbooks

Similar questions

1. Basic Integration a. fx(x + 1)dx b. [√x+x² dx C. ·√₁² |x-1|dx
iz #11 ist 2 3 4 on 5 K Evaluate. 2 0 √2x dx 2 √√2x dx = [ 0 -(Type an exact answer in simplified form.) < Quest
Solve the problem by using Exact DE 3 1. (2 x³ x y² - 2y + 3) dx − (x² y + 2 x) dy = 0
Solve for k such that 1 k(x2 – 2x + 1)dx = 5 3.
[4] PLEASE PROVIDE THE CORRECT AND SOLUTION. (kindly provide complete and full solution. i won't like your solution if it is incomplete or not clear enough to read.)
i need the answer quickly
Suppose you are working for a manufacturing company that is analyzing a newer product using the following: A=πr2 dA/dt=2πr(dr/dt) Explain what the product engineers may be examining/testing/analyzing. Why is the factor dr/dt needed?
Q3 Find and show the work for (а) 2 (x+3)(3x+2) dx. (b) SF (sin(2x) – cos x) dx.
1. (a) Consider the following integral: tan (3z) sec (3x) dr. (i) By using the substitution u = 3a. transform the original integral in the form f(u) du. Write down /(u). (1i) Start with part (i) and use d sec u and solve the integral in terms of u. (iii) Hence evaluate tan (3r) see (3.r) dr. (b) Let m and n be integers such that 0
Use integration by parts to establish the reduction formula: To begin the integration by parts, let u = Evaluating du = de and v = -0 leads immediately to the above reduction formula. [(lnx) dx = x(lnx)" - n f (lnx)n-1 da: and du = dx. Now apply the reduction formula to the problem: (In x) dx. Getting the final result would be tedious, requiring 9 applications of the reduction formula. So for simplicity just give the result of applying the reduction formula one time. (In 2) da is simplified to +10 dx +C.
APPLICATION 1. Find the antiderivatives of the following functions using the substitution rule. Write your answers on a separate sheet of paper. a. [(5x + 4)5dx b. √ √4x-5dx c. sin¹0 (x) cos(x) dx d. fdx II. Find and correct the mistakes in the following "solutions to these integration problems. Write the new solutions in the space provided below. a. [sin 5x dx;u= 5x, du = 5dx sin 5x dx = = [₁ sin u du = -cos u + C = -5 cos 5x + C 9 cost_dx;Mm. sản x, du = cosx dx 1+ an cos x du -dx = 1+ SIR²X 1+u² c. f(4x + 1)(2x² + x) dx;u= 2x² + x, du = 4x + 1 [(4x + 1 x + b. = In||1 + u²| + C = In|1+ sin³x|+C 1)(2x² + x) dx = [uħdu = ²(2x²+x) + C