When using Bernoulli's DE, the resulting DE is often what type? Separable DE O Homogenous DE Linear DE O Exact DE

Q: Compute the given integral. ICOS Idz +C

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Q: The set of all values of p which makes the integral x* dx is divergent is a) (-1, 0) b) (-n,-1) c)…

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Q: By reversing evaluate LE O the order of integration double integral cos (x²) do dy LE

A: Hello learner we can answer first question as per the honor policy. Please resubmit other question…

Q: Prove that cosh-z = In (z + vz? - 1) %3D

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Q: Find y(0), y(1), y(e), y', y", and a formula for y(") where n is a natural number. Use DNE, Does Not…

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Q: The particular integral of (De +1)y= cosx is O None of the choices zsinz 2 ICOSI 2 ECOSI 2 O zsinz 2

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Q: Calculate Hhe fourier coeffrecents Of the fancdion fR) over the nderval -スと×L2 here: Fx)=(0,-2くメCー…

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Q: What type of DE is the following? xydx + (x2 – 3y)dy=0 O Bernoulli in x Bernoulli in y O Linear in x…

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Q: 21. Prove that lsio rol ylanoti (i) Res (tan z, x/2) – – 1 1-cos z (ii) Res 12

A: The solution is given as

Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: Compute the given integral. 5x°e3 dx %3D +C

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Q: (C) The evaluation of the integral S. de is 0 cos3e (i) 글+in 3 3. 4 (ii) +=In 3 4 3 (iii) None of…

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Q: Find the differential cquation a the (2.K) families af cirdes with center at and wi th radius r

A: To find: Differential equation of circle with centre 2,k and radius r. We know that equation of…

Q: and let ah -(-1'I Let In tan (a) for n = 0,1, 2 Intz 1) Show that In + Io+ り+! (-1)" for nal an-…

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Q: By using the Integration by part 9. udv = [vu] v du for the following integral 1 | x In(4x) thẹn the…

A: The integration by parts method is used to integrate the product of two functions. The integration…

Q: The DE : y = e-/Y is seperable Select one: O True O False on

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Q: The Fourier cosine integral of J (x) D 0, 2, 0<x<3 is 0<x О а. 4sin(@)cos(@x) do O b. 8 sin(3@)…

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Q: FOo=X-1 de fined 2n E- lro] show that Fis Riemenn integruhk

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Q: At the point of discontinuity on (0, co), the Fourier Cosine integral corverges to: f(x+) – f(x¯)]…

A: We have to solve given problem:

Q: Evaluate the integral. Oin | +0 | C In (x-8)² x + 7 In |(x-8) ³² (x + 7) + Din ((x=83² ) +1 In C + 7…

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Q: Evaluate the integral S CO|CT CT | CO CT /Co NIC 8 dx using the two-point Gaussian quadrature rule.…

A: We have to evaluate the integral ∫−22816+x4dx using the two-point Gaussian quadrature rule. Here,…

Q: Find the product of the integral 1- S x²cos(xy)dxdy

A: We have to change order of integration first.

Q: Q: Prove the trans ferm; formula's by definition of Lapia (Dirac Delta fauncden) %3D

A: A delta function is defined as δ(t-a)=0     for t≠a∞   for t=a      . The fundamental property of…

Q: Prove that E (2s+l)=3n" whenever 'nisa psitre r'nisa pisitive intger. 32.

A: Given that,      ∑j=n2n-12j+1=3n2, n is a positive integer

Q: Find the solotion of the differential eaoation thot satisties the qiven nital condiion

A: The given differential equation is,

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

A: Prove,∫z=1dzz2 sinh z=-πi3 ∫z=1dzz2 sinh z=∫z=1fz dz .........equation 1 fz=1z2 sinh z , 0&lt;z&lt;π…

Q: 5. 9 ycotx %D CSC

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Q: The given integral is equal to cos 3t dt 5 + 3 sin 3t O (1/3) In 15 + 3 sin 3t| + C O (1/9) In 15 +…

A: To find out the integration.

Q: dy then In z is If y = cosh z

A: Without wasting any time, any further, differentiate the RHS to get your answer.

Q: Compute algebraically the resultant of the following complanar displacements: 100 N at 30°, 141.4 N…

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Q: Use Romberg integration to compute R3,3 for the following integral S²x x³ cos x dx

A: Given integration is I=∫01x3cosx dx For n=1 sub interval h=1-01=1 Then by Romberg  method…

Q: Evaluate the iterated integral. • In10 Ins e*** dydx eIn10 rIn5 eitty dydx = i

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Q: Evaluate: (2x + 1)3 dx by two methods: 11) let u = 2x + 1 %3D 12) Expand (2x + 1)³ Compare the…

A: Integration

Q: 5. Evaluate the integral " Vtan o dex 1. de in terms of beta and Vtan gamma functions.

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Q: Which of the following is NOT true about the DE: 6x²ydx +2x*dy=0?

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Q: nsi Sinhna (na)? 8. ) Sind( x) Sin y)

A: Given Fourier series, ux,y=∑n=1∞1sinhnπ8sinnπ2nπ2sinnπ2sinhnπy2+8nπ2-8cosnπnπ2sinnπx2sinhnπy2 To…

Q: Can i get help step by step with this problem?

A: Given:

Q: Use Euler-Maclaurin's formula to prove that E n %3D

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Q: Provide a homotopic squared parameterization of side one o_1= [-1,1] x [-1,1], other than this, and…

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Q: iv) Sº³ §¾½5 √xª + 1 dxdy

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Q: 8. Evaluate the iterated integral. /8-z2-ya zdz dz dy

A: The given question can be solved as explained in step 2.

Q: Prove that the area of the cardioid 3 r = a(1- cose) is , πα?. 2

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Q: Use Romberg integration to compute R3,3 for the following integral cos x dx

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Q: D Find a singular saluhion of DE: %3D

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Q: Use Romberg integration to compute R3,3 for the following integral x cos x dx

A: Romberg integration is one of the way to approximate the value of definite integrals. In this…

Q: Evaluate the iterated integral 3 1/x 4 = S S yla³ dydæ 1 1/22

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Q: 1 +y = zy" dy dr

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Q: Evaluate the triple integral [[Scosys3 12xy²z³ dV_over the rectangular box G define by the in…

A: We have to find value of given triple Integral.

Q: determine the area inside of the inner loop of the limaçon r = 2 cos 0 – 1.

A: We have to find area of r= 2cos(theta)-1

Q: Prove,J w' Sin wx du %3D COSZ 2

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.