Let C be the shortest path that connects a to ni and I = S, (coshz – 1)dz. Then %3D O I=-sinh n+ n(i-1) O I=0 O I=-1-cosh n+ n(1-i) None of these |=-sinh n+ n(1-i) O I=-1-cosh n+ n(i-1)

Q: 2) (D² +6D+91)y= 16e-3x x² +1

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Q: Find sec42x -dx tan 2x A --—-—-cot²2x-—-—-cot³21+ C 16 cot82x) (4sec22x-1) B -(cort2x) 4 12 11 1 C)…

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Q: (ax-3 (x+4)8 Degreez co EGAelents

A: The detailed solution is given below Thank you

Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

A:

Q: dy If y = (5x + 1)(2x +In x), then will be %3D dx (5x + 1) +) + 5(2x+ In x) A. -1 B. (5x+ 1) - 2. +…

A: The given problem is to find the derivative of given function y=(5x+1)(2x-1+ln(x)) , we can use…

Q: /s. 5. Show that 2x?dx = f 2x²dx + S, 2x²dx + f 2x²dx %3D

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Q: Evaluode Lim [x]+[2x ]+ n2

A: We know that, x-1<x≤x Therefore, 2x-1<2x≤2x ⇒3x-1<3x≤3x . . . ⇒nx-1<nx≤nx ∴ (x + 2x + 3x…

Q: What is the value of k if any So kxe* dx = 1

A: This question is taken from the Definite integral in which we have to find the k value by solving…

Q: Let 7 (t) = < - 2 cos(2t), Find F(t)dt (don't include the +C)

A: Please refer to the image below.

Q: If csc e = 1/3t, then where defined, cos 0 A) Square root of (1 – 9t²) 3t/squareroot of (1 – 9t2)…

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Q: 110. π/3 -π/3 /sec²x - 1dx

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Q: 4 sin (2x) dx cos (2x)t4

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Q: Differentiate. Find ele ele ele ele ele AP O AP O for y=x-1 Whatsa AP O 2x³ - 3x² (x −12 - 2x3+3x2…

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Q: Find the general solution for the following ODE. State which rule you are using. If the initial…

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Q: dy 2 3 ...2 C05X +sinx...y.-(4x+5). y. ---

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Q: Find the general solution for the following ODE. State which rule you are using. If the initial…

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Q: 7s+15 Find L-1 s+2 O 7 cos (v3t) + sin(v3t) O 7 cos (v2t) + sin (v2t) O 7 cos (v2t) + sin(v2t) O 15…

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Q: 3. ſ(4 csc2x cot2x + 2sec² 2x)dx A. 2 tan2x – 4 csc2x + C C. tan2x – 2 csc2x + C B. - tan2x + 4…

A: To evaluate:∫4 csc 2x cot 2x+2sec22xdx

Q: 9. Use a trig substitution to show that f steps. dx (1+x²)3/2 = √1+2+C. Be sure to clearly show all

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Q: For the given function 6=x²yz C=3x²yi+yz²j-xzk and Find 82 Sysz (c) at point (1, -2, -1).

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Q: ifferentiate the funtion y = 2 csc (1-3x)

A: Giveny=2cosec(1-3x)Aim: dydx

Q: Find L[t sinh 6t] 12 (s²+36)² 12s (s²–36)2 12s (s²+36)? 12s (s²–36)? O O O

A: We know that the Laplace transform; Ltnft=-1ndndsnLft And Lsinhat=as2-a2 Given: Ltsinh6t

Q: 8tan4x dx. Q. S 3 None 8log|sec4x| + c 3 2log|sec4x| + c 3 2log|sec4x| + c 4

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Q: Differentiate y = In x*V1-3x (2x-1)2 4 A. 4 | 1-3x 2x-1 4 4 1-3x 2х-1 4 C. X 1-3x 2x-1 4 D. +. 1-3x…

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Q: Use the identity cos alpha cos beta = 1/2[cos(a-b)+cos(a+b)] to rewrite 2cos3xcos2x as a sum of trig…

A: The given identity

Q: 14) In isosceles AABC, A is the vertex. AB=2x+7 BC = X+IS AC SX-2 a)wrrte an equation that could be…

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.