2. Let f and g be integrable functions such that f(x) dx = 6 and g(x) dx = –2. Using the Linearity Properties of the Definite Integral, compute | (3f(x) – g(x) + 5) dx. -

Q: Find the Particular Integral for the given differential equatiorn d²y dy +3- dx +6y =2x²+x+5 dx2…

A: using expansion,         (1+x)-1 =1-x+x2 -x3+...

Q: 10) Suppose that f is continuous and that f(z) dz = 0 and f(z) dz = 5. Find - 6f(x) dx . -3 -3 A) 30…

A: ∫-33f(z) dz = 0  ,    ∫-35 f(z) dz   = 5find -∫356f(x) dx∫abf(x) dx    = ∫acf(x) dx   +∫cb f(x)…

Q: ! 6-Find the value of the integral * U x3/2 e-x dx

A:

Q: The value of the definite integral' f(x )dx for f(x) = 3 is:

A: We are going to evaluate the value of the given definite integral for f(x)=3

Q: 10 Suppose that " fx) dx and Ax) dx = -5, and "g(x) dx = -1 and g(x) dx = 3. Compute the given…

A: Given,∫04f(x)dx=7∫02f(x)dx=-5∫04g(x)dx=-1∫02g(x)dx=3

Q: 3. Use the Comparison Test to determine whether the integral cos? x dx is convergent or divergent.…

A:

Q: If g(1) = -1, g(5) = 2, and | g(x) dx = -9, evaluate the integral %3D æg'(x) dx.

A: Given: g1=-1  and g(5)=2∫15g(x)=-9

Q: Let H(x) integral ,for -2 ≤ x ≤2.Find the value of s such that H(x)= sH(-x).

A:

Q: Find the most general antiderivative of the function g(x) 3x2 -e + coS I | O 6x-ex-sin(x)+C O…

A: The given function,  g(x)=3x2-ex+cosx  .................................(1)

Q: a) If | f (x) de f(x) dx = 2, find 1 (3f(a) – 1) de. = 7 and || - /4 (b) Estimate the value of the…

A:

Q: 4- 2x Evaluate the following integral : dx 2x +4,

A: The answer is π/3.

Q: dx. Evaluate the integral / (x² + 1)(^ · x – 2) -

A:

Q: 2. Evaluate the improper integral. e COs x dx

A: I=∫0∞ e-x cosx dx Integration by parts;Formula:∫(uv)dx=u∫vdx -∫dudx ∫vdx dxu=cos x, dudx=-sin…

Q: 1. Approximately compute the value of the following integral, as accurately as possible, using the…

A: Note:- Here, you mention function f(x) is creating little bit confusion for me. Is…

Q: 1. If f(x) dx = 3, evaluate [[1 + 21(x)] dx using the properties of interga 2. If f(x) dx = -2 and…

A: As asked we can answer question no 1 and 4 as below.

Q: evaluate the given integral.

A: Use Substitution method to determine the value of  integral .

Q: 3. Evaluate the following improper integral; -2 2 dx x² – 1

A:

Q: Evaluate the integral. HINT: 3 x2 dx J2 x - 1

A:

Q: 2. Evaluate the integrals. (a) S (b) [9rc (c) J (d) O 1+ e²r 9x cot(x²)dx -do -dx cos sin² 0 +1 -dx…

A: As per the guidelines we can solve 3 parts only

Q: 3. Suppose f(x) dx = 8 , f (x) dx = -2, g(x) dx = 3 Evaluate the following integrals: a) 3f(x) dx =…

A:

Q: Find the integral of (1 2x) e^ (-x) dx from x-0 to x=. с. 2 А. 3 в. 4 D. 1 O B

A: ∫ uv dx = u ∫ v dx - ∫ (u' ∫ v dx) dx. ∫ (1+2x)e-xdx = -(1+2x)e-x + ∫2e-xdx ∫ (1+2x)e-xdx =…

Q: 2. a) Compute the integral fa f(x) dx using 5 point composite rectangle, trapezoid and Simpson rules…

A:

Q: 1. Evaluate the following integrals: S; dx -x² + 4x - 3 f) . dx (x − 2)√√x² − 4x + 3 -

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: Evaluate the integral f 2x (x² + 3)° dx using the substitution u = x2 + 3.

A:

Q: C for the con

A:

Q: c) Suppose fand g are integrable and that S(x)dx = 4 , [ f(x)dx= 6 , [ g(x)dx= -2. Find the…

A:

Q: Evaluate the improper integral e-1/x dx

A:

Q: f (x) = = cos 2x; [0,T] G and

A: topic - mean value theorem

Q: 6. f(x)dz = f(t)dt, If what are the bounds of integration for the first integral? = and b =

A:

Q: e*dx e2x +1

A: We know that; ∫axdx=axlna+C And ddxcot-1x=-11+x2   Given: I=∫7cot-1exexdxe2x+1   ....1

Q: Evaluate the integral x3 dx 2+100 S x3 dx +100 (Use C as the arbitrary constant.)

A: Given,

Q: 3. Suppose that f and g are integrable and that f(x) dx = -1; , f(x) dx = 5; and f, h(x) dx ='4,…

A:

Q: 3. Evaluate the integrals. dx ( Use u = Vx(1+x)

A:

Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

A:

Q: Q1)Evaluate the following integral: 2 1-x dx 1+x2,

A: 1 We have to evaluate the integral ∫021−x1+x22dx. Now,…

Q: 11:32 E O 1 Evaluating the integral f In(x)dx, where x> 0 yields:

A:

Q: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

A:

Q: Evaluate the integral. S(e* +8e -*) dx | (e 4x +8 e -x) dx =[(Use C as the arbitrary constant.)

A: Consider the given integral.

Q: 9. In evaluating the improper integral dx , which of the following is true? (1– 3x)2 3 (A lim 3x 1…

A:

Q: If - 2 f(x)dæ f(x)dx + f(2)dæ – / f(x)dx, what are the bounds of integration for the first integral?…

A: We have to solve the integration

Q: 2. Calculate the following transcendental integrals: a) S² exee* dx X b) S (x²+1)In (x²+1) dx cos…

A:

Q: a) [ ]: Evaluate the integral (4x + 1) In x dx c) [ ]: Evaluate the integral 2 dx (x – 1)(x + 4) |

A:

Q: Q1. Evaluate the integral S dx (x + 1)(x² + 1)

A: We need to evaluate the following integral ∫01dxx+1x2+1

Q: (b) Evaluate the integral | xe * dx. (1- x)?

A: Given : The integral is ∫ xe-x (1-x)2 dx .

Q: f(x) dx = -3, f(x) dx = 8, and g(x) dx = 8, find the following integrals. If 1. f(x) 2. + 6] dx =

A:

Q: 3 Suppose that f(x) dx = 7, | f(x) dx = 5, and | f(x) dx = 10. %3D Evaluate the following definite…

A: (a) The given integral is: I=∫35f(x)dx As we know from the integral theorem,…

Q: Let f(x) = x³+1, x<1 1 X+4 5 1.8976 x≥1 Use the composite Simpson's rule to approximate the integral…

A: Introduction: The formula for Simpson's 1/3rd rule is given by,…

Q: Evaluate the improper intergal 1 dx using the residue (x² + 1)3 theorem.

A:

Q: Find the integral [(x** +(-1)°x*!) In((a+2)x)dx b+1 с+1

A: The integral has been solved n attached in the second step.