Find the most general antiderivative of the function g(x) 3x2 -e + coS I | O 6x-ex-sin(x)+C O x3-e*+cos(x)+C 3.

Q: Find the family of antiderivatives for each ofƒ(x) = ex, g(x) = 4x3, and h(x) = sec2 x.

A:

Q: Find a function f € span(1, cos x, sin x) which minimizes the integral 2πT √²* |x +1 − f(x)| ²dx.

A: Given a function                     f∈span1, cosx, sinx

Q: Find the antiderivative of xe2x/(1+2x)2 from 0 to 1/2

A: Given the integral ∫012xe2x1+2x2dx

Q: true false f(x) = R x −100 cos(t)dt and g(x) = R x π cos(t)dt are both antiderivatives of cos(x).

A: f(x) = R x −100 cos(t)dt and g(x) = R x π cos(t)dt are both anti derivatives of cos(x).

Q: 2 3x 2. Evaluate f x'e* using integration by parts.

A:

Q: 6. Let a be a positive constant. Determine the general antiderivative of a using the fact 1 a² + x2…

A:

Q: 9. Find the most general antiderivative of the function a) f(x)=12+ sin x b) f(x)= 3x(x-5)

A: see below the answer

Q: f) y= xcos(xln x) g) y= 3(sin 2x – x* }** In. 3x'e** h) y= cosx

A:

Q: Integrate the function. 16x +즐 + C V16 -2 8 sin 1 +C 2 V16-2 +C + 16V16 - x2 8x - W16-2 +C

A:

Q: Match functions ƒ with their antiderivatives F. F (x) = cos (11 – x) F (x) = -11 cos (x) F (x) = -…

A: use substitution method and product rule for finding the antiderivative.

Q: 2xージ f (x) : 33 Vx2 T sin 2x + Ve2x + 2x –- In e, x # 1 1-x (1–3t)5(t³-8) g(t). t # 2 2-t

A:

Q: 9 Evaluate the integral f 2x (x² + 1)° dx using the substitution = x² + 1. и — с 2.x (x? + 1)° dx +C

A:

Q: What is the antiderivative of 1 / (x - (1/k)x^2) with respect to x? k is a constant

A:

Q: 11. Find two different antiderivatives of the function f(x) = 6x² +2ex. 1

A:

Q: 12. Show that F(x) = sinx – x cos x+2 is an antiderivative of f(x) = x sinx.

A: Given, F(x)=sinx-xcosx+2 To show that the above function is an antiderivative of f(x)=xsins.

Q: 9-x2 18-x²-y² xydzdydx. B: Find the integral fo J

A: Triple integral

Q: For the following integration / sin"(24x) cos(24x)dx what is the suitable substitution? a.…

A:

Q: Find the general antiderivative of f (x). f (x) = e* – 6 sin (x) - (Express numbers in exact form.…

A:

Q: 1 Find the most general antiderivative of the function x3 + 4x

A:

Q: 6. The coefficient of Sin(x) in the antiderivative of F(x)=| is

A:

Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: A b B d a The integral 15x²x³43x - 19 (x + 1)²(x² - 6x +13) can be rewritten as Ax + B D C + ax² +…

A:

Q: (9) Evaluate the indefinite integral f X+2 dx x² + 4x 2

A:

Q: Find the most general antiderivative of f(x)=−7x^2+8x−2. Note: Any arbitrary constants used must be…

A: An anti derivative of a function f is a differentiable function, whose derivative should be equal to…

Q: x²dx Evaluate the integral V16 – x2 O A. 16 sin-1 (프) - 4x +c O B. sin-1(플) +c O C. 2 sin-1 V16 – æ2…

A: We use trigonometry substitution.

Q: Find and show the work for 2 (x+3)(3x+2) dx. (a) (b) SF (sin(2x) – cos x) dx.

A:

Q: 3. The integration of x e* with respect to x is: A. e2x. В. 2хе* С. 2

A: To integrate  xex2 with respect to x: ∫ xex2dx Apply u-substitution: u=x2 Differentiate both sides:…

Q: Find the critical numbers of the function. b) g(x) = |2x + 3|| c) f(e) = 2 cos 0 + sin2 0 d) f(x) =…

A: gx=2x+3 fθ=2cosθ+sin2θ fx=x lnx

Q: Find the general antiderivative of f(x) = 2 cos (x) – 7 sin (x) and check the answer by…

A: For a function g(x) if f(x) is the derivative of the function such that ; d(g(x))dx=f(x) Then;…

Q: 1. Find the general antiderivative. A. S 5x8 4x4 + 10x3 – x² – 9x + 15 dx В. /2 - cos x + sec x ·…

A:

Q: 10. Find the most general antiderivative; verify your answer by differentiation. 5-4x 2x" b) f(x)…

A:

Q: Find the antiderivative for the given function. 3x tanh(x*) 1) In(cosh(x*)) +C 2) In(cosh(x*)) + C…

A:

Q: Find the general antiderivative of f(x) = 4 cos (x) – 11 sin (x) and check the answer by…

A: given that:       f(x) = 4cosx - 11sinx we have to find first,   ∫f(x)dx then after we have to show…

Q: Find the most general antiderivative of: f(x) = 4√x − sec(x) tan(x) + (7/(x2+1))

A:

Q: Find the linearization L(x) of the function at a. f(x) = cos(x), a = 3n/2 %3D

A: We have to find the linearization L(x) of the given function.

Q: Find the most general antiderivative of: f(x) = 4√x − sec(x) tan(x) + (7/x2 +1)

A:

Q: 2. Use integration by parts to establish the reduction formula: Sx" cos x dx = x" sin x – n x"-1 sin…

A:

Q: Let f(x) = 9 · 5" ln(5). Find the most general antiderivative. F(x)

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the different…

A: The annihilator of xn-1 is Dn The annihilator of xn-1sin βx is D2+β2n Now the given function is…

Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

A:

Q: 3. Find the general antiderivative of f(x) = x² + 3x+4 sinx.

A:

Q: Find the Wronskian for y, = sin 3x , and y2 = cos 3x.

A: The Wronskian, W, of two functions, f and g is calculated as follows. W=fgf'g' , where, f' , g'are…

Q: -X +7 Evaluate the integral: dx (x-2)(x+3) In x - 2|+2 1n x +3 +C 2 In |x – 2| – 2 In |x + 3|+C 2…

A: First of all we will do partial fraction, then we will evaluate the integral.

Q: 10 Evaluate the integral f 2x (x2 + 4) " dx using the substitution u = x² + 4. 2x (x² + 4)*" dx =|…

A: The given integral ∫2xx2+410dx

Q: Find the general antiderivative of f (x) = 4 x ln x²

A: Given: fx=4xlnx2

Q: Find the most general antiderivative of f(x) = sin x cos x .

A:

Q: 1. Use algebraic manipulation and (if necessary) u-substitu- tion to integrate the function. (a) /…

A: Hey, since there are multiple questions posted, we will answer the first three subparts of the…

Q: Integrate using substitution method a. S (x² – 2x)(x³ – 3x²)²dx ( sin(In x) b. dx с. f (2х — 3)-7dx

A: (a) ∫ (x2-2x) (x3-3x2)2 dx            x3-3x2 = t        (3x2-6x) dx=dt      3(x2-2x) dx =dt…