Prove that S. 8 dx √π 2

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Q: If n is an odd natural number prove that I =, xsinnx dx = sinx 2.

A: Consider the given: It is given that n is an odd natural number, Take n = 1,Substituting n=1 and…

Q: 2 1-X ie 2=tny then prove that da

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Q: trace the equation in 3 -dimension

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Q: Solve the equation tan 3x = √3/3  on the interval [0, 2π).

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Q: Let A denote the 2 x 2 matrix We define a function (, ) : R² ×x R² → R by taking (x, y) = y" Ax, for…

A: We have A=1221. We are given the function ·, · : ℝ2×ℝ2→ℝ by taking x, y=yTAx, for each pair of x,…

Q: Suppose z and y are funetions of time and satisfy the formula e sin y = In y + tan dy Write a…

A: Solution:- differentiate with respect to t.

Q: 3) Evaluate ex*+¹sin (√x) dx].

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Q: 1. In section 5.8, we saw that f du = tan-u+ C. Use a u-substitution, then this formula, to u?-…

A: topic - indefinite integral

Q: Let 2 A = 9. -1 (a) Show that A 3 (2+3i) 3

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Q: Show thatI cos ve (-1/4s)

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Q: 1. D, [3x²y+In(xy²)] За + In(xg In(xy³)]

A: Given,

Q: b) Prove that, S∞ (@3x+1)² dx e2x 2π 9√3

A: Let we get, Let We get, This implies, This implies

Q: 3. V4- (x – 3)²dx.

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Q: du Given u In[y cos(3x²y)1, solve CoS %3D ax

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Q: Q) prove that (1) -2P xSinx 2.

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Prove that there is a real number r so that sin(r) = x – 1.

A: We have, sinx=x-1 Let us consider a function fx such that, fx=x-1-sinx

Q: e²x Prove that, (e3x+1)² fo - 8 dx 2π 9√3

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Q: B 2. 7.2.Preve that CD= 24 SnR Vzt2 cosx

A: Use trigonometric ratio to solve

Q: lim 0 2 + sin(okr }) k=1 6 O A. J(x + sin(2xx)) dx 6 O B. J(2x + sin(2xx)) dx 3 O C. J(x +…

A: Definite integration limit as sum

Q: Show that 2π de (5-3 sin 0)² 5T 32

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Q: Prove that 55 sin x² dx - 5 cos x² dx = 1/2 √

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

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Q: Prove that d/dx [cos x] = −sin x.

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Q: 3 T Compute sin 4

A: Let the given sin value be y -y = sin-3π4y = -sin3π4                                 sin(-x) =…

Q: 4.) Compute the following: x sin 2x dx x2 +3

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Q: Find So Cosx (x² + 1)² - ex

A: We shall be using basics of residue calculus to evaluate this integral

Q: | cos (70 + 5) de

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