2FI 2 sin nx dx cos nx dx =0, where n integer. %3D !! 0.

Q: Describe the method used to integrate sin" x cos" x, for m even and n odd.

A: The method to integrate sinm x cosn x when m is even and n is odd. We integrate by substituting the…

Q: 1. -5 cosh x 2+3sinh x dx

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: If y = (2x)sin (4z) , then dy sin(4æ) · (2sin(4z) esin(4z) In(x)) %3D dx X synta

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Q: 2FI 2FI sım nx dx = cos nx dx = 0, where n integer. 0.-

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Q: 2cosx dx 2 5- fn 1+(sinx)? π

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Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

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Q: 6. S 2sin´x sin(2x) dx

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Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: what is the antiderivative of   (sinx/1+cos2x) dx?

A: Let,

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

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Q: S sin 2x sin 4x dx 7.

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Q: 4. X sin (x) dx VI-X 1-メ-

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Use the trapezoidal rule withn = 4 to approximate 5 cos(x) -dx- Keep at least 2 decimal places…

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Q: Find the area.   y = 3 cos(4x),    y = 3 − 3 cos(4x),    0 ≤ x ≤ π/4

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Q: 10. Find , if y = dy 1-cosx dx 1+cosx

A: Given  y = (1- cosx) /(1 +cosx) To find dy/dx

Q: Find for y = 5x sin x+ 10x cos x- 10 sin x. dx Dikdörtg

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Q: (雲) 1 dy tion 1+ is = 3 dx wy da 3, 1 12, 1 1, 15 15, 1

A: We have to choose the correct answer

Q: fxcos 73 x cos 4xcos 2xdx π ſcos(nx)dx 75 ーπ 77 xsin(nx)dx

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Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

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Q: S sin3xsin 2x dx 3.

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Q: 2 | (sin³x cos x + sinxcosx)dx 7/2 π

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Q: (27 (b) Show that 0. 4 tanh- 2x dx In 8. 16

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Q: 3. S In(cos x) tan x dx

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Q: Ni cos(2?)a. Cos | x dx

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Q: 36. sin x dx, with 6 rectangles using the Right Hand Rule.

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Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: (a) S sin³ cos dx . 3

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

Q: S sin(4 + 5x) cos (5x – 4)dx

A: From the given problem: I=∫sin4+5xcos5x-4dx As we know that the trigonometric identity:…

Q: 4 The range of y =sinx for 7SXS is 2 0syso 4 <ys0 sys1 ys 4 -1sys,

A: We are given a function y(x) = 4/5 sin(x) and we need to find the range of y(x) when π ≤ x ⩽3π2 (…

Q: 2cosx dx 5- ? 2 1+(sinx)2

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Q: 3. In (cose) tane de

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Q: Given the integral sin(3x + 5) dx cos(3x + 5)

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Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

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Q: aluc of 4 alue of dx. 1+(x – 2)? 1

A: See the details solution in below

Q: sin ydy (4 + cos y)²/3

A: We know that integration of xn is xn+1/n+1 +C. Here C is integral cosntant.       Here i attached…

Q: Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0…

A: Please refer the attached image for complete solution.

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

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Q: 16. S sin 3x cos 3x(cos 3x+1)² dx

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Q: 2.1 Given that 1 sinh x show that dy cosh a. dx

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Q: 2. S sin*(2x)cos²(2x) dx 4

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Q: 7)(x+tan y) dy sin 2y dx

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Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts, ∫cosn x dx=cosn-1 x sin…

Q: 4. EVALVATE | sin4x vos5x dx

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Q: 211 3- sin nx dx [1-cos2nx]dx 1t, where n integers.

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Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: S secs/2 (금x) tans (글x) dzx

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Q: integral from 0 to pie over 4 of sin^2 (4x) cos^2 (2x) dx

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