Section 5.6 Homework-MARIA ANASTASIADIS Google Chrome xlitemprod.pearsoncmg.com/api/v1/print/math Print g(b) 3. Use the Substitution Formula, f(g(x)) g'(x) dx f(u) du where g(x)= u, to evaluate the following g(a) a integrals 2 sin 2t) cos 2t dt а. (1 (1+sin 2t)cos 2t dt 0 3 (1 sin 2t)cos 2t dt а. (Simplify your answer.) (1+sin 2t)cos 2t dt b. д 4 П к 1ч

Q: 1 2 de 4-cose %3D II

A: Given,          ∫0π214-cosθdθ

Q: determine the annihilator of the givenfunction. F(x) = sin2 x cos2 x cos2 2x.

A:

Q: What is the solution of a 2nd order homogeneous linear ODE whose roots of the characteristic…

A:

Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

A:

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A:

Q: 1) x² cos 2x – 3x

A: D2 annihilates x D2+43 annihilates x2cos(2x) Hence D2(D2+4)3 annihilates x2cos2x -3x

Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0 |

A: We will find out the required solution.

Q: By using first fundamental theorem of calculus. Solve the problem 1.) Suppose f(x, y) = S*3 If fx…

A:

Q: cos(rw) 1+w²

A: Fourier Cosine Transform or Infinite Fourier Cosine Transform: Definition: Let be a function defined…

Q: If the RHS (Right Hand Side-the source) function of a second-order differen tial equation with a…

A: Here we have to go option wise and choose the option with; y(0) = y'(0) = 0. Clearly we can see…

Q: FULL SCREEN PRINTER V Chapter 6, Section 6.6, Question 055 Use integration by substitution and the…

A: Given integral,

Q: EXAMPLE 1.13 Determine the particular solution of an ODE subject to given initial condition sinx dy…

A:

Q: 41-44 Use Theorem 13.5.3 to find dy/dx and check your result using implicit differentiation. 42 x3 –…

A: Implicit differentiation

Q: QUESTION 4 Suppose that x2 -v3 +2xy= 12. Use implicit differentiation as presented in Section 14.5…

A:

Q: (1+cos(4t) dt 2

A: Let's find integration of given function.

Q: 41-44 Use Theorem 13.5.3 to find dy/dx and check your result using implicit differentiation. 41. x²y…

A:

Q: -1-3x+ e3X ) im x>0 hint: L'Hopitals Rule - cos(x)

A:

Q: Reduce the following partial differential equation to a canonical form and hence solve it :…

A: The objective is to solve the partial differential equation, uxx-2sinxuxy-cos2xuyy-cosxuy=0

Q: Integrate with respect to x: sin(3r) b 2 cos(4x) cos²(2x) a

A:

Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

A:

Q: Transform (cos x)^2 to 1/2(1 + cos 2x) Transform (sin x)^2 to 1 - (cos x)^2 All options are…

A: Given that In the integration of (cos x)^4 (sin x)^3 dx, what is the appropriate transformation?…

Q: determine the annihilator of the givenfunction. F(x) = sin x cos3 x.

A: We have to determine the annihilator of the function: Fx=sinxcos3x Annihilator is the set of linear…

Q: Chapter 6, Section 6.3, Question 014 Use the Fundamental Theorem to evaluate the definite integral…

A: Given,

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Evaluate ∫2x4x2-1dx          ...(1)

Q: Substitution review Derive integral formula 14 in Table 8.1: tan ax dx = -In|sec ax| + C. a

A: Given: verify that ∫tanaxdx=lnsecxa+c we know that tanθ=sinθcosθ

Q: 41-44 Use Theorem 13.5.3 to find dy/dx and check your result using implicit differentiation. 42. x'…

A:

Q: Question 3 If f(x) = f A sec ³x 1+elanx B 1+tan²x 1+etanx In (secx) √ 1+tan²x C tanx 1 + e sec²x D…

A:

Q: Find a linear differential operator that annihilate the given function d) Sin5x + 10 cos5x e)…

A: (d) Given that y=sin5x+10cos5x We have to find a linear differential operator that annihilate the…

Q: Put the given differential equation into form (3) in Section 6.3 (x – x,)?y" + (x – x,)p(x)y' +…

A: Given that x2−1y''+3x+1y'+x2−xy=0 Here, smaller x0 value is -1 and larger x0 value is 1 Now,…

Q: determine the annihilator of the givenfunction. F(x) = x cos 3x.

A: Consider the given function, F(x) =x*cos 3x. Let f(x) is a function, which is defined as,…

Q: Integrate with respect to x: sin(3x) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

A: We have to solve the following integral .

Q: · /9" cos(1 – f') dt 17. 9t" cos

A:

Q: In the integration of (cos x)^4 (sin x)^3 dx, what is the appropriate transformation? * A.) All…

A:

Q: Find the critical numbers of the function

A:

Q: 7. Show that the integral equation R has no eigenvalues. g(x) = a √ (sin x sin 2t) g(t) dt

A: Hint: The given equation is g(x)=λ∫0π(sinxsin2t) g(t) dt First suppose C=∫0πsin2t g(t) dt then…

Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

A:

Q: Chapter 6, Section 6.3, Question 013 Use the Fundamental Theorem to evaluate the definite integral…

A: Consider the integral

Q: 1- ( 5*-1)d xt (2xy-SinyJelya0

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Activity 2 Differentiate the following. 1. y = sin(6x) 2. y = sin (5x – 2) 3. y = tan (2x³ + 5) 4. y…

A:

Q: Question 2 Calculate the given integral: / sin“ (6x) cos³(6x) dx 1 1 a) O30 cos (6x) – cos'(6x) + C…

A:

Q: Example 1 Find dy/dx, if a. y=sin(x² + 3x + 1) b. y = cos² (2x-1)

A: I have stated the used formulas in the solution

Q: Use (1) in Section 6.4. x2y" + xy' + (x2 - v2)y = 0 (1) Find the general solution of the given…

A:

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Given, I=∫25325dxx25x2-1

Q: 6. x sec x tan x dx

A: Let's find.

Q: 1. 6. dx (x – 3)²dx V1+8x -1 2. 7. 3 x²dx (5– 19– x²) dx 3 1 (1- х3)2 -3 3. 8. 3x 1 1dx -dt t4+t² +…

A:

Q: Question 6 Compute the following integral: sin (8z) de 1 4 a) cos(8x) sin*(8x) + C 32 1 cos (8r) + C…

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.