7 4 In GL(2, Z13), det 1 5 11 9. 35

Q: L{t + et} =+ I. L{t + e3t} = = 1 %3D II. S-3 52 5-3 L{t + e*} =+ L{t + e#} = - III. IV. S+3 52 543

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Q: 20.tvaluate :L[t cosh 14t] A, 3s? +19le s²+196 C. (5?-1967? (6?-196)? -s?+ 196 s?-196 B. D.…

A: Using property of Laplace transform

Q: 1. Evaluate (i) dy dx, 3

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Q: h) Ž() Sn

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Q: 8/ Salve the fellow ing DE O x+ dy=2

A: According to our company policy we can only answer the first question and rest can be reposted

Q: Evaluate the integrals

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Q: S cFinz (Inz + 1)dz

A: Given: 7. ∫azlnzlnz+1dz To Find: To evaluate the given integration.

Q: If z = x2 - xy + 2y² and (x, y) changes from (3, –1) to (2.97, –1.05), compare the values of Az and…

A: Recall the definitions of dz and delta of z. We will need the basics of differential calculus and…

Q: • In 3 6te'i + 7ej+2 ln tk dt

A: Here we will evaluate the given integral.

Q: 2. S 22+3x dx = 4 ( +c In 8.

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Q: 1) z = e(4+j3) lIn(6230°)

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Q: 2. J Зу /7—Зу?dy

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Q: Determine L '{F}. s?F(s) s+5 + 3sF(s) – 10F(s) = %3D 2 s+ 6s

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Q: 4 2 To find the blue shaded area above, we would calculate: b. f(x)dx = area a

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Q: 9. G. 61° %3D mGK %3D (9x- 22) (5x - 7)° mHJ %3D MHGJ = K 34° MGKJ %3D

A: As per the company's guidelines, we are supposed to solve first question for you kindly repost other…

Q: Runge from d tep siz SİZ

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Q: 8. What is the rate of change of the edge length s of a cube Vith respe ds С. ds D. dV 1 ds В. dv…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Calculate SN given by Simpson’s Rule for the value of N indicated.

A: In this Rule, N is an even number and h = (b – a) / N. The y values are the function estimated at…

Q: 45. у 3D VI + * dt

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Q: Evaluale the to 312 bwiny dx 12

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Q: 18) S cot z + 2 dz 2 Csc Z +

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Q: 2. I cosh ix dx

A: The given integral is ∫cos14xdx. Evaluate the integral.

Q: dz IV100-49(In z)?

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Q: mZQ = 41 57 T S. mZR = %3D 137 mZS = %3D 9:4 Sign out

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Q: = e. In(16y), then fzz i 30 e5z In(16y) 25 e5z In(16y) 80 esz In(16y) 25 e In(16y)

A: We have to choose the correct answer from the given options according to the given information

Q: 5= 36-t sVE +at FND ds

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Q: nitial ter t und?

A: The distance s from the ground is given by;s(t)=96+80t-16t2When, ball touches the…

Q: If z = 3x2 + y² and (x, y) changes from (1, 3) to (1.05, 2.9), compare the values of Az and dz.…

A: Given, (x,y) changes from (1,3) to (1.05, 2.9) f(x,y) = z = 3x² +y²

Q: Exeraise 3: Use Charpit's method to Salve the fallowing EDE: -0.

A: Given equation is, x2ux-x2uy+uuy2=0 The charpit's method formula is,…

Q: 1. S 7!nlsin(@)l cot(0) de 2. S(r + 1)2r*+2r dr 3. S 3w 2w dw

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Q: L{e¬at cosh bt} = %3D

A: The given function is e-a tcosh bt. The main objective is to evaluate the value of Le-at cosh bt.…

Q: e of x to the nearest tent 8. 12 8

A: Using Pythagoras theorem , Hypotenuse2 = base2 + perpendicular2

Q: 8. dy de = azte-c 2-ex

A: To Solve: The differential equation dydx=x2+e-xy2-ey

Q: 1. b. X %3D in

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Q: (z In z + 5)dz

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Q: 2 for z = 1.21, o, = 0.76, 02 = 0 62, n, = 15, and ng = 49 n2 Evaluate E=z %3D E= (Round to two…

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Q: evaluate the indefinite integral.

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Q: A roctangular tonk uith a cauaro boco and a volumo of 2.016 e3 dimoncions of tho tank that hac 1o…

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Q: 6. Evaluate 1 x² + y² + x² dV, where E = { (®,g, z) |1< n? +g? +z? <4}.

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Q: In(rºs sºVr?s²) 6,8/7 2 r'S is equal to A In r+ B ln s where A = and where B =

A: using the concept of logarithmic...

Q: •P R S. T OP with mTOR = 0

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Q: dy a a 1+ Vy + 1 5+ aln:

A: First I have used a substitution and make integral easy and then solved it.

Q: 9. For what value of k, k> 0, does (4kx-5k) dx = k² O 1 O 2 3 O 4

A: On solving this we will get

Q: In csch 4y d 3) tanh 4y

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Q: N 25 )X= 125 SX2 = 650 EY2 = 460 EXY = 508 t was, however, later on discovered at the time of…

A: Given: N=25 ∑X = 125, ∑Y= 100 ∑X2=650 ∑Y2=460 ∑XY=508 Two pairs are taken as (6, 14) and (8,6)…

Q: d 53. cosh? (9 – 31) = –6 cosh(9 – 3t) sinh(9 – 3t) dt

A: Given derivative is ddtcosh29-3t.

Q: 2 3 4 To find the blue shaded area above, we would calculate: | f(x)dx = area Where: a = b: f(æ) =…

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Q: 1. [ 8re" dt

A: The integration by parts formula is ∫udv=uv-∫vdu . We have to use the differentiation formula…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.