Integrate the following: 1. 1+x² dx (1+x)³ 2. sin5 cos5 x dx

Q: dx Perform the Integrations 1+ sin x+ cos x

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Q: Evaluate the integral.

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Q: Find dy/dx for the following : 1) y = x3 + sin x² + sin-1 5x 2) y = 32x + In (sin x²) + In(sin-1 5x)…

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Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: dx 3 cos x+2 sin x-5

A: This integral can be solved by using the trigonometric formulas of sinx and cosx in terms of…

Q: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

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Q: FIND DY/DX OF THE FOLLOWING -y=sin' In (x+1)

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Q: Evaluate ]e * cos (7x) dx. Seex cos (7x) dx = %3D

A: Explanation of the answer is as follows

Q: sinh x dx 1+ cosh x

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Q: Integrate cos2x/sin^2(2x+8) dx

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Q: J cos 2x sin 3x dx

A: To find: The integral of ∫cos2x·sin3xdx. Formula used: Trigonometric formula: 2cosA·sin…

Q: Integrate: So a sin(x²) dx

A: We have to integrate

Q: Evaluate cos √6x dx using a substitution followed by integration by parts.

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Q: Compute d/dx  sin-1 (x/x+1)

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Q: Evaluate the integral: 2 sin(3x)cos(3x)dx A B 1 4/6 —— 1 wlr 3 1 - wlw

A: Given ∫π3π2sin(3x)cos(3x)dx

Q: If y=(sin3x-cos3x)², find dy dx

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Q: Q1\| Integrate SIX of the following functions: sinh(lnx)dx 1) 3) | sin?(2x).cos(3x) dx 2) ex. sinxdx

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Q: Se* sin e*dx

A: We have to find integrating of given Questions

Q: Find integral.

A: We have to find the integral I=∫cos(5x) dx

Q: Find 17. d Ssin (4x) cos(4x) dx

A: Use substitution to solve

Q: So sin¹ (6x) cos (3x) dx

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Q: dx Sin cosx 2.

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Q: 3. Integrate the following dx (i) V9 – x² (ii) ſe-3*cos4x dx (iii) ſ sin³2x dx -

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

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Q: -2 Ssin®(3x)cos(3x) 5 dx

A: Given, ∫sin53xcos3x-25dx We have to find the integration.

Q: find dy / dx by implicit differentiation.

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Q: Use the first two non- zero terms to estimate ∫​sin(x^2)dx from 0 to 1.

A: Solution:- Use the first two non-zero terms to estimate ∫01sinx2dx

Q: Integrate: x² cos(2x) dx

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Q: 1. Calculate the Integral sin x cos x dx

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

Q: Compute for the arcsinx dx . Which of the following is not an antiderivative of the function f(0) =…

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Q: Estimate 1 7 cos(x2) dx 0 using the Trapezoidal Rule and the Midpoint Rule, each with n = 4. (Round…

A: I=∫017 cos (x2) dx             f(x)=7 cos (x2)b=1, a=0, n=4h=b-an=14=0.25aThe Trapezoidal…

Q: Calculate L{e-# cos(2t – r)}

A: We have to calculate : Le-2tcos(2t-π) First we will calculate , Lcos(2t-π)…

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your du? du = x…

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Q: Find dy/dx for following functions. 1) y = csc-(e2inx?) + sin-1(2lnv3x)

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Q: Integrate the following functions: 1. S sin 2x dx

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Q: sinx dx (cosx

A: The given integral is ∫sinxcosx2dx.

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

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Q: find dy dx ² +F y = 3 casch + Cosa 3 and x = Sin²³ o

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Q: Find the trigonometric integral ∫cos3( x − 1) dx

A: Find the trigonometric integral ∫cos3( x − 1) dx

Q: Use integration by parts to evaluate 16r cos 4r dr.

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Q: find dy /dx for the following 3 2 -1 Y3x'+Sin x+ Sin5X

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Q: 4-3x dy dx X,

A: its a multiple integral based question.so 1st we integrate with respect to y and then with respect…

Q: find dx 20. 19. 0 do 21. 22. dy -2x sin 2x dx cos 3x dx 23. 24.

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Q: Integrate x cos(2x^2+7) dx. Select the correct response: O sin (2x^2+ 7) + C

A: Integrate using substitution method.

Q: Evaluate / e*cos(x)dx using integration by parts-

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Q: t/2 SL cosx/1+ cos²xdxdy is equal to 0, siny

A: Consider the iterated integral, ∫ab∫f1xf2xfx,ydydx In this iterated integral, the integration is…

Q: da (cos ( 3x) sin( 2æ)) dæ

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