1 2. Evaluate =dx using the trigonometric substitution x= 2 tan0. 2 Vx + 4

Q: 4x +1 = cos y?

A: According to guidelines we should have been able to solve only one question at a time

Q: S .2 4. sin x cosx dx

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Q: 4. Se2x sin(3x) dx

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Q: 1 |+tan¬(x), then x2 dy If y=cot-= dx

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Q: 4T then 3 If 0 = sin(0) = %3D Give exact value.

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Q: 2 6. dx (sin x – cos x)?

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Q: x = cos(30), y = 2 sin(0).

A: The parametric equations are given as, The the corresponding derivatives are calculated as,

Q: 3. Given the equation y = In(cos(x)): What is dx/dy? secx -seox -tanx -cotx None of the choices.

A: I am attaching image so that you understand each and every step.

Q: 6. Identify the proper trigonometric substitution and then solve the integral 1 dx (x² + 1)²

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Q: The x2- 4 dx can only be evaluated using trigonometric substitution technique . A True B) False

A: To find if the given integral can be solved only by algebraic substitution technique.

Q: Evaluate the integrals

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: • T/2 (3 + 7 cos³ x) sin? x dx

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Q: 23. Determine the period and amplitude of the function y = 2 sin 5x. 3x D. 2 3x 10 c. 3.2

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Q: 2m 14. sin x dx

A: Topic- trigonometry  note- As per our guidelines i have to do only one question other can be…

Q: 15.y = C1eª×cosbx + C2eax sinbx ; a and b are parameters

A: Given:   y = C1 eax Cosbx + C2 eax Sinbx

Q: 1. Find 2 for y defined implicitly by the equation tan(x?y*) = 3x + y?

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Q: Q(1) Find [cot( cos-(x²)] dy

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Q: 2) Find of the following equation then simplify whenever possible. and dx dx2 x = 1+ Sin t y = Cos?…

A: The given parametric equation,   x=1+sin t, y=cos2t

Q: 9. If I = 4 sec22(x) tan36(x) dx = uP (1+u²)ª du , then la a = b p I| || || I|

A: We have to find a, b, c, d

Q: 3.x cos 5x dx 5. ( re'/2 dr

A: 3.Integration by parts;∫ uv dx=u∫v dx -∫dudx∫vdx dxI=∫ x cos5x dxu=x, v=cos5xI=x∫cos(5x) dx -∫ (1…

Q: B) Find and if x sin 3z and y = tan 3z dx

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Q: Eliminate the parameter: x = cos3 t and y = sin3 t.

A: Given: x=cos3t                                               ..1y=sin3t…

Q: 2. Find cos ec (In x) dx . x1+ cot(h x)

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Q: 4 Find (b) y sin 2x.

A: This question is about differentiation or finding derivative of y with respect to x.

Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: e the equation on the interval 0S0<2x 2 sin 0+4 = 5

A: We have to find angle theta

Q: Demonstrate and derive the following Bernoulli's Equation. - 2y tan x = y² tan²x dx

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Q: 4 Find (b) y = 9. sin 2x.

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Q: 1 2 1 sec? nt) tan (nt Ttt ) Ttt ) dt 0.

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Q: dx 5) prove that sin x+c using method of trigonometric substitution. %3D

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Q: 3) Solve S(4cos? x+4 sin? x)dx

A: Given:

Q: The period of y = 3 cos 5x is 2 7I 2 T/5 2 1/3

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Q: 4. Find du for the equation 3y? – cosy = x° -

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Q: T/2 ( 4 cos (x) sin° (x) dx

A: To evaluate the integral ∫0π24 cos2(x)sin3(x) dx We know that, cos2(x)=1+cos2x2sin3(x)=3sinx-sin3x4…

Q: S 4 cos (x) sin (x) dx = %3D

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Q: sốn ² sin () cos() sin() dx (Consider initially the first 2 terms)

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Q: Given: = 0 – sin 0; y=1– cose Find: dz2

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Q: 3 Cos |X TT 13) y = 3

A: We need to plot the graph of given curve:

Q: 6. Find dy/dx and simplify y sin = - х

A: According to our policies we are allowed to solve one question at a time so kindly repost other…

Q: dx = ? 4 sin x – 3 cosx+5

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Q: Evaluating 9-x² dx using trigonometric substitution will lead to: A of th (A) cos²0d0 [*/ cos²0de Ⓒ…

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Q: Q: Evaluate : fe 1- cos 2ax dx. 1+ sin 2 ax 2ax

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Q: (7/6 sin t dt cost 39.

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Q: 1. Evaluate 9/ COS x (a) (1 – x)e dx (b) ,"™ dx p) A-2 sin r -

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Q: B) Find and It x sin 3z and y= tan 3z dx

A: x=sin23xy=tan 3xWe need to find dydx and d2ydx2.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.