Evaluate the following integral e-24 8(t – 1)dt A) e-2 B) e² C) e-1 D) E) 0 e

Q: S(9i + 3tj + 7t k) dt. -1

A: The given integral ∫-119i+3tj+7t6kdt Integrate by taking dot product with idt, jdt, kdt

Q: Evaluate the integral. 8e 8t dt 8t 2. 1+ e 8t 8 e dt = 8t 1+e

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Q: Find the formula for the function represented by the integral 1 -dt= 5t+1

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Q: 2 sinºe cos³e de= 60 a O 120 b O 1 .c O 60 .d O 120

A: We have to solve given problem:

Q: 2 20 Let A = Which of the following is a consequence of the Cayley -Hamilton Theorem? 2 10 L-10 0]…

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Q: 2) Refer to sections 1,2,3 in the course notes. Compute the integral: S (3e' – 4 )dt

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Q: The answer of the integral St v7e + 12 dt is ( + 12)2 + c + 12)/2 +e

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Q: e3t dt 2 (1+4e*)

A: Please refer the attached image for complete solution.

Q: 5. Use Taylor's theorem to write down an explicit formula for R, (1). Conclude that R, (1) + 0, and…

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Q: 8 Use the Cauchy integral formulae to evaluate 22 – 1 - (9 – 22)(z + 2i))³ | where C is a circle |z…

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: 3. Compute the given integral. S 7x³e2*dx = +C

A: The expression of integral function is .

Q: Let A = d e Assume that det (A) = -13, compute the following.

A: Properties of Determinants :If we given A , nxn matrix then i) The value of det(cA) = cn det(A)…

Q: Prove if equal to MPn (W) dx= 2" (n!)" (2n+)! that m is an integer

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Q: Find f"() if fx) = 2e* - %3D e* In 2 Ob) 20 2e* O c) 2e O d)

A: Recall:     d(eax)dx=a.eax

Q: 3.3 5t – 3 dt 2t° – 7t

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Q: (a) Let a > 0. Using the substitution t = In x or otherwise, prove that In a e 4/a² - e 2t dt =a5…

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Q: 2 a) Evaluate the following integrali. D √²8 (4-2) Cosa=t&t DS sct-2)8(t-1)dt 3 √ (t²+3+) alt-Idt.

A: Solution a: By the fundamental property of delta function ∫-∞∞fxδx-adx=fa          (1)

Q: 10. Find the integral| dt. t* +81

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Q: 1)z = e(4+j3) In(6230") 2) z = (-;)(* 2) z = (-)(r)"

A: (1) The  given complex equation is                                                Z=e4+j3ln6∠30°

Q: S eln (1-t) 1-t - dt ed to you in any form

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Q: Evaluate the integral. (1s - t )dt t + 8 -2

A: Given that the integral is ∫-2016t5+18t4-tdt. It is known that ∫xndx=xn+1n+1+C.

Q: Let a be a constant. Given that 3x In(ax)dr = e18 ( 36 -89 , find In a. 3

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Q: B// Evaluate the following integral: fx³ n* dx.

A: We integration by parts and logarithmic properties  eln(x)= x  ln(mn)= n ln(m)

Q: A sufficient condition to use Newton's progressive formula for inclusion is: Xnxo (A) m = |m| < 1 n…

A: Solution:-

Q: Evaluate the integrals

A: Solution -  Given Integral equation - y = ∫π201+cos2t2dty =12∫π20dt + 12∫π20cos2t dtUsing…

Q: Evaluate the integral. 1 √2√2 ²² √2-4° dt t³

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Q: Evaluate the given integral. 2"s(t)dt - 00 9e"8(t}dt = - 00

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Q: 4 16 Define T: R? - R° by T(x) = Ax, where A = 1 3 -

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Q: Compute the given integral. fGz (6z - 5) (32- 5z + 2)"da | +C > Next Question

A: The given integral is ∫6x-53x2-5x+212dx.

Q: Evaluate the integral. 8t 8 e S dt 1+ e 8t 8e 1+e 8t 8t dt =

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Q: 2ху 3. y' = -x?

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Q: Consider the following integral: +oo J(2a) = | - dzerp(-20r") / dyezp(-2ay7) = { / drerp(-2aa")}?…

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Q: Integrate the following: ,S (x4 – 5æ³ + 6) dæ - 1. So(1- r)*dz su(1– 2.

A: These questions are related to indefinite integration, we will use use integration formulas and…

Q: Evaluate the following integral. 2x e 2x e + 4 2x e 2x +4 е

A: Take the integral S e2x        . dx e2x  + 4 For the integrand e2x          , substitute…

Q: 6. Use Green's Theorem to evaluate O (y* – xy?) dæ + (2 – a*) dy where C is shown below. y -2 ² +y²…

A: Green's theorem

Q: Verify that u' (t – a) = 8(t – a) by solving the problem x' = 8(t – a); x (0) = 0 to obtain x (1) =…

A: What is Laplace Transformation: Laplace transformation is crucial for control system design. Laplace…

Q: Evaluate the definite integral. el8# i+ e*j+t k )dt O el8 i+ (e" – 1) j+ k el8 – 1 18 O el8 - e i+k…

A: The definite integral,      ∫01e18ti+e-tj+t kdt

Q: | 45. Apply integration to the expansion 00 =E(-1)"x" = 1- x+x – x +.. 1+x n=0 to prove that for -1…

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Q: 13- dy + 2xy = y diferansiyel denkleminin genel çözümü aşağıdakilerden hangisidir? -x* +c1 y = e a)…

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Q: z'e? dz

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Q: 1. Prove that L(t)=. s2

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Q: et + 6e3t + 12e2t +9e dt. (d) Evaluate the integral / (e2t +4et +5)2

A: First, simplify the integral. As the degree of the numerator is greater than the denominator, use…

Q: Show that (D+ 3t)D , is not the same as D(D+3t), where D is the differential operator.

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Q: Solve the glven differentlal equation by using an appropriate substitution. The DE Is of the form Y…

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Q: 1. Compute e? and In (z) in the form a + jb, where z equals to. i. 3+ jn ii. V2-j ji. j TT 1

A: It is required to find ez &amp; lnz for the given complex numbers. A complex number z=a+jb can be…

Q: Evaluate the following definite integral e-(s-2)t, -(s-2)t sin(3t) dt. 3 2 (s – 2)2 + 9 (s – 3)2 + 4…

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Q: Evaluate the integral. 7e 7t dt 7t 3+ e'

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Q: A resistor of 500 ohms and an uncharged 5 x 106 farad capacitor are connected to a 100-volt battery.…

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Q: Evaluate the integral 8t (181² – 3)î + 1?+ 1 t k dt 12 + 1 /

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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.