| sec (3.r)dr reduction formula (or any other method) =)dx = 1 sec"-2 (ax) tan(aæ) + (n – 1)a n- 2 %3D xp(= sec"-2 n- 1

Q: The lowest point on the graph of y = cos x, 0sxs21, occurs when x=

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Q: T/3 4 sin x -dx 1-4cosx

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Q: sec x=1/5 on [0,2pie)

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Q: 1. 2. (√ex + (ex)³) dx /22sinx cos x dx

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Q: dp Find dx given p(x) = (sin?(3x))(3x²-4*)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Product rule: f·g'=f'·g+f·g' The Power rule;…

Q: x- 3 +C 4 dx3D - 17+6x – x² +3arcsin = - V7+6x – x²

A: Show that ∫x7+6x-x2dx=-7+6x-x2+3arcsinx-34+C

Q: | – (3x² sin x + 2) dx In r dx Je

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

Q: xsin ax 2 2 (x²-x²) 1/2 Show that [²= - dx - TV J₁ (ay) 2

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Q: 8. Find for y=√√4x (arcsin(x²+2x)) dx

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Q: I/3 1 dx Ja16 \1+ tanx. R/6

A: SOLUTION:Given let   I = ∫π6π311+tan xdx= ∫π6π3cos xcos x+sin xdx=12∫π6π32cos xcos x+sin…

Q: Evaluate (a) ſ In(2x + 2)dx /3 (b) [ sec'3x tan 3x dx

A: Please see the answer in step 2

Q: 6. Find : (a) y = (x +5) tan 7x, %3D dx

A: Given :y=(x3+5)tan7x

Q: /2 3 d.x 2 cos x +1 -7/3

A: Given, ∫-π3π232cosx+1dx We have to evaluate the definite integral.

Q: a) Find for 5x² – x³ sin y + 5e*y = 10 dx

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Q: Find the derivative. 5х + 1 In 5x - 1 dx 5x +1 %3D dx 5x -1)

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Q: (a) (b) So (arcsin x)² dx 0 L cosh² x dx 2

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Q: need the answer as soon as possible

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Q: 3 dx x2 + x – 2

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 3. (D² + 1)y = sec² x tan x. %3D

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Q: /3 dx cos x tan x /4

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.