1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de Ob. lim 5 sec-'(4/5) tan-' ((b+4)/5) d0 С. lim b→∞ J tan-1(4/5) O d. 1 lim 5 b→0 tan-' ((b+4)/5) do tan-(4/5)

Q: Use Simpson’s Rule with n = 4 to approximate ∫1  ex^2dx

A: The given function is continuous on the interval [0, 1], then using Simpson’s rule to find the…

Q: Evaluate the integral. 3 1 3y2 cos xy dy dx x/3 5(1 - cos 3) 3(1 - cos 3) cos 3 - 1 (1 - cos 3)

A: Formulae used: ddxxn=nxn-1∫cos(ax)dx=sin(ax)a+C∫sin(x)dx=-cos(x)+Csin(0)=0cos(0)=1

Q: Evaluate the definite integral S (1+ 2x) dx using Riemann sum.

A:

Q: Show that integral - infinity  to infinity  x dx is divergent.

A: We will evaluate the limit of the integral using two different routes and see if we get the same…

Q: Evaluate the double integral sin(y' +1)dydx.

A: Use the change of order of integration to solve this problem.

Q: Give the general antiderivative for the integrand in the definite integral cos x + dx.

A: give the general antiderivative for the integrand in the definite integral

Q: Find General Solution on this Diffential E Qution by using (uC set) =e +Sin X

A: Given differential equation is y''+y'-2y=ex+sinxfind the general solution

Q: Evaluate the integral ,(1 – x – 4x³ + 2x³) dx a) Analytically b) Single application of trapezoidal…

A: we have  f(x)=1-x-4x3+2x5 we need to find ∫-24f(x)dx  a) analytically b) using trapezoidal rule

Q: (5) Find the indefinite integral (a)f Vtan x sec²dx (b)fem2* sec² 2xdx sin x (c) Cos x 1 cos-do 0 2

A:

Q: Evaluate the integral. arctan dx 1

A: For evaluating the given integral, we will use the concepts of integral by parts and integration…

Q: 2.) Evalvate the Integral ودل أاد-ل (x² _33² dx, .3 2 by making w - x²-3 NOTE: Answer should be in…

A:

Q: 5. Evaluate the indefinite integral. S cososin'oc (1) (3x - 2)20 dr (2) (3) S etanr sec?rdr

A:

Q: Find the integral m tanx X, 1+x?

A: Given :

Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

A:

Q: Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) trapezoidal rule, (4) parabolic…

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: Use any method to evaluate the integral. 6 dx explam why 3 ton euas used as ithe substitution x= (9x…

A:

Q: dx so that the resulting integral is integrable? What should be the rewrite of the integrand of…

A:

Q: Evaluate the iterated double integral √1-x² _L [ ³²-x² sin (x² + y²) dz dy dx

A:

Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

A: To find the integration

Q: 3 Which of the following is equal to / sec 2 x tan³x dx to obtain the correct indefinite integral? A…

A:

Q: Evaluate the double integral 1 2x+1 LL.** Select one: | None of them 113 x² dy dx

A:

Q: 10. Prove by using integration by change in variable the ff. integral: dx du = arcsec x + C xVx2 - 1

A: To show∫dxxx2-1=sec-1x+C.

Q: Only one of these calculations is correct to evaluate the definite integral Inx dx Select one: 1 Inx…

A:

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. |x…

A:

Q: 19. Use Simpson's rule with n=8 to estimate the following integral. Estimate your error. So5-4 cos.x…

A: Given integral can be evaluated by using Simpson's rule with n=8 as shown below

Q: Calculate the approximate to the integral -5 (24 +2x² − 3)dx, by the composite midpoint rule with…

A:

Q: Evaluate the integral 3 2x cos(xy)dydx 2

A:

Q: Evaluate the integral. 3y- cos xy dy dx x/3 O 5(1 - cos 3) O 3(1 - cos 3) O cos 3 -1 (1 cos 3)

A: Given: ∫03∫x313y2 cos xy dy dx We have x3≤y≤1 and 0≤x≤3 This can be seen as: We can change the…

Q: Consider the improper integral: x² +2x+2 dx what will be the appropriate solution and answer? A Im…

A: ∫0∞1x2+2x+2dx

Q: Evaluate the Integral dx – (**V2Tan-1x-(Tan-1x)2 1-х4 '2Tan-1x-(Тап-1x)2 3. S х?/2Tап-1x- (Тап-1x)2…

A:

Q: At the point of discontinuity on(0, 00), the Fourier Sine integral converges to: OA None f(x+) -…

A: Here  At the point of discontinuity on  0,∞ the Fourier sine integral converges to

Q: 7. Use integration by parts to prove that for any positive integer n, | cos"x dx = 1 cosn-1xx+ n - 1…

A:

Q: Use the Midpoint Rule withn= 3 to approximate the integral %3D 13 (- 9z - 3a")daz 9x 3x) dx

A:

Q: Evaluate the integral (8 (8x+15y)dx + (27x - y)dy along the parabolic arc y = x² from (0,0) to…

A:

Q: Find the indefinite integral. Solution in handwritten. 1. secy (tany - sec y ) dy

A:

Q: 7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x|…

A: Given that: (a)∫4x+sec2xdx(b)∫1xlnxdx(c)∫x4-3x2+5x4dx

Q: (b) 3 – cos(x) 2

A: Follow the procedure given below.

Q: If the substitution x = sin y is made in the integrand of . - A dx, the resulting 1-x integral is

A: Put value in  given  integral

Q: 4. Evaluate the improper integral. dx х2 — 1

A: Consider the given integral as Solving the integral

Q: Show that integral 0 to infinity  x2 e -x2  dx = 1/2 integral 0 to infinity e -x2  dx

A:

Q: Which integral computes arc length of f(x) = x5/2 on [0, 1]? 1 49 -x' dx 1+ 4 - 1 | V1+ x° dx 1 1+…

A: We have to find the arc length

Q: Jcos(2x)+ sin(0.5x) Using riemann compute for the integral of F(x) = tan(3x) sum over the interval…

A: We can solve this using Riemann sum

Q: 9. Use Simpson's Rule to approximate the integral f Vx3 – 1 dx withn = 6.

A: We have to find the value of given integral using Simpson's rule.

Q: 4 -dx is divergent. 1-2х (b) Show that the improper integral

A:

Q: Evaluate the integral (i) S3x3 sin 4x dx (ii) ſ In (x³ + x) dx (ii) cot-1 2x dx (iv) ſeax cos bx dx

A:

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z2 sinh z Where 0 < |z| < T.

A: Use the following formulae, to evaluate the given complex integral. Let z0 be a pole of order n,…

Q: 2. Evaluate the improper integral S₂ (5. dx (5-x)4/3 or state that it diverges.

A: The given integral,      ∫28dx5-x43

Q: Consider the curve given by f( x ) = 4 cos( 2.5 x) on the interval 0 sxs 2 n. 4 1 -1 -2 -3 -4 1 4 6.…

A:

Q: Give the general antiderivative for the integrand in the definite integral (cos +1)dx. cos x

A: Simply integrate and put the limit than simplify.

Q: Evaluate the definite integral S (1 + 2x) dx using Riemann sum.

A: