5. Express 0 lim E (5x2 – 9x +16)Ax;[ – 8,4] as a definite integral. L (5x – 9)dx b. l' (10x – 9)dx a. L (5x² – 9x + 16)dx a.I"(5x² - 9x + 16)dx 9. The expression is a Riemann sum approximation for b. b Vīdx a. c. 818

Q: Q.3 Find the double integral for Sl. x2 dydx, where R between y = -4/x y = -x and x = -4

A: Ti evaluate the given double integral  first we draw  the region

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: G.. Evaluate the fallowing real integrals by residue. theerem 3 -bm e 응) co3 mx (x4a?) Cx+b?)

A: This is complex analysis problem, we apply the residue theorem to solve the problem.

Q: 4 18. Evaluate the indefinite integral / dx. 3 X,

A: Given integral to find ∫4x3dx To integrate this first take the constant out 4∫1x3dx Applying the…

Q: According to numerical methods, the integral of a function f(x) over the limits a and b can be…

A: Given data  Used Simpsons 1/3 rule  f(x)=7e^(-πx)(sin(x^2)) With a=0 and b=2 and number of intervals…

Q: Q3. (30pt) Calculate the integral 2x³ – 4x + 1 - (1– cos x) dx 1+x? a) for n= 10 according Simpson…

A:

Q: The particular Integral for (D² + 19²)y = sin19z is Yp 38 O Yp 19 O None O Yp Zacon19z 38

A:

Q: 8. Determine the number M and the interval width h so that the composite trapezoidal rule for M…

A:

Q: 3 2(x²+1)7 Write down an integral that gives the ARCLENGTH of y on the interval from x = 0 to x = 2…

A:

Q: The area between the curve X= t2 - 2t+1, y= In(t) and the y-axis for 1sts5 would be found by setting…

A:

Q: Determine whether each of the following integrals is proper, improper and convergent, or improper…

A: We need to determine  whether each of the following integrals is proper, improper and convergent, or…

Q: Use residues to evaluate the improper integral [a+x2/1+x4]0∞dx; where a is a real constant

A:

Q: Determine the following integrals: 1.1 G 3x³ +8 X dx 1.2 G 1.3 4x+6 dx x + 3x-10 sec² (sin 5x)cos 5x…

A: We have to find out solution

Q: 00 1 (b) Calculate the improper integral dx , or show that it (x² + 25)3/2 -00 diverges . Show your…

A:

Q: Evaluate the integrals ∫cos (1 - ln y)/y dy

A: We have to find the integrals: ∫cos1-lnyydy We will find this integrals by substitution method Let…

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

A:

Q: 3. Evaluate the double integral /sin(x+y) dx dy by using Simpson's 1/3-rule with four sub-intervals.

A: I = ∫0π2∫0π2sin x+ydxdy,

Q: 8. Depending on the real parameter p and q, what can you say about the result of the following im-…

A:

Q: 3. Prove properties (3) and (4) analytically, by making x = -t in the part of the Integral from -a…

A: Concept:

Q: 2. (a) Show that when x > 1, In(x) (This should be very short.) (b) Use your knowledge of integrals…

A: We have to show below given expression

Q: Q2:- Apply romberg's method to the integral of f(x) = nx*cos(-Tx to 2 with Tol = 10-4

A: Given function is f(x)=14πx4cos14πx, we have to integrate above function from 0 to 2. Formula for…

Q: Consider , xe¬**dx. What will be the appropriate solution and answer to this improper integral? A.…

A:

Q: aluate the Cauchy principal value of the given improper integral. dx (x² + 1)²(x² + 9)

A:

Q: 3) Approximate the value of following integrals by using composite Trapezoidal rule, composite…

A:

Q: 2. Evaluate. the fallowing.integrals.a.fter.seveoiag.the areler.of.integratiam. dydx Ans..In)/4 C.…

A:

Q: d) Numerically approximate the integral 2+ cos(2Vx) dx by 3 Simpson's rule with 6 strips

A: Given integral is ∫022+cos2xdx. To evaluate the integral using Simpson's 38 rule. Consider the…

Q: 1. Use integration by parts to find the integral below. In(x19)– 9x10+C a. b. x ·In(x1)– 10x10+ C c.…

A:

Q: 1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de…

A:

Q: 3.12 Еxpress lim n00 n k3D cos 1+ as an integral. (Be sure to include the lower and upper limits|of…

A: Given: limn→∞ 2n∑k=1ncos1+2kn To convert this into the integral , use the following method

Q: (5x° + 4x + Ix Consider the indefinite integral dx x2 – 1 Then the integrand decomposes into the…

A:

Q: , 1. Take the following integral numerically using an end corrected method. (n-7, h=0.001) (give…

A:

Q: Compute the approximation  of the integral -4 to 4 e^(-x^2) using the trapezoid rule with n=4; you…

A:

Q: 6. Evaluate the fallowing real integrals by residue. theerem 3 -bm -am 응) Co3 mX ans : X Sin mx ans…

A:

Q: Find the value of the improper integral or state that it is divergent. (If it is divergent, enter…

A: We will calculate the definite integral using basic definite integral properties and if we get an…

Q: 3. Apply Romberg quadrature to •1 1 dx 1+ x2 for h = 1, 1/2, 1/4, 1/8. Show a table of approximate…

A: We are given the following definite integral : ∫1/(1+x2) dx from 0 to 1 And we have to solve it…

Q: 2- Approximate each of the integrals in the following problems with n = 4, by (i) The trapezoidal…

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

Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

A:

Q: 2. Set up an integral to find the exact length of the curve defined by 1 f(x) = 1 In r 2 - 4* where…

A:

Q: Evaluate the integral: sinh 3x csch 3x dx coth 3x "+C 3 coth X +C 3 - coth x +C - 3 - coth 3x +C 3

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: (b) Approximate the definite integral f"/² cos(x)dx by employing the Composed Midpoint rule with n =…

A:

Q: 3. Estimate the integral v2 + x² dx using appropriate of Simpson's rule with step size, h = 0.2.

A:

Q: Q5. Approximate the integral Sin(2x)dx (i) Using composite Sympson's rule with n = 2,4 and

A: As per the policy of bartleby the provisions is to solve only one question at a time so I am solving…

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: 1. Evaluate the integral 2 8x cos y dy dx y – 4 by reversing the order of integration.

A:

Q: 1.Evaluate the following integrals and check using differentiation: d 5-5t dt 10 +2.12e- . (a) 0.5t…

A:

Q: 2. Evaluate the following Integral by using suitable method: 2y3 + y y4 + y2 + 1 dy -

A:

Q: /4 1.* Use the following property of the definite integral to estimate the definite integral:JCcos x…

A: