Q-1: Integrate the fraction of functions: 1. f- 14a+1 2. sinx- V(1-x) 2-7x-4x2 dx 3. SE 1-sine dep. cos²0

Q: sin 3t dt J cos 3t – 1

A: Given: I=∫sin3tcos3t-1dt   ....(1)   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx, where…

Q: O. p. S sin 2x cos 3x dx 3dx /1 + 9x²

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Q: Solve d²y dx² - cot x dy-sin² x.y = cos x - cos³ x. 2 dx

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Q: B. By miscellaneous substitution (VE+1)dx dx 1. S 2. S: 3 cos x+2 sin x-5 XA +

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Q: Q3- Find i) S sin3x.cos(-5x)dx

A: We have to evaluate the following integral: int sin 3x . cos (-5x) dx

Q: Integrate: So a sin(x²) dx

A: We have to integrate

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

A: Note: -     as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 2. Evaluate J dx (cos³x sin³x)

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Q: Q#2 (a): Find root of the equation 3x + sinx – e* = 0 by secant method correct to six decimal Places…

A: # we are entitled to solve 1 question at a time ,please resubmit the other question if you wish to…

Q: Integral of Sin^2(2t)cos^2(2t)dt

A: Given: ∫sin22tcos22tdt

Q: Using Variation of Parameters 4y''+4=cos-1x

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Q: a) (sinx + cos 2x)dx (+1) do b) S dx c) S (x+2)(x2-6x+5) 8 cot(In 8)

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Q: olve the equation on the interval 0s0<2x V2 sin0- sin 0 = 0

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Q: 5 sin“(3t) dt

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Q: Q No 4) Integrate S cosec³xdx . AND also Find F sin10xdx

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Q: V sin2(x32 - 1) dx, with u x32 - 1

A: Consider the integral ∫(√x)sin2 (x3/2 - 1) dx.

Q: (- + 2 cos 2x ) dx + (- - 2 sin 2y ) dy = x2

A: You have asked multiple questions in a single request. As per our honor code, we will only solve the…

Q: Find dy/dx of y=sin-(1/,). 9x-

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Q: COSX sin x dx 4. S 1-ఆశి అరికి న

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Q: cos2x a) -.dx,b) xe*. dy Į sin2x. [In(sin2x)]² + sin2x 0.

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Q: Find d-/dx² at the given point without eliminating the parameter. x=0+ cos0 and y=1+sin0 ; 0 =a/6,

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Q: csch (2 sin2x) dx 1. V1-4x² r(²-1)cos[cosh (In r)]dr OS 4.

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Q: e2x dx 1. Зе2x+1 2. sinx dx 1 3. cos 2x

A: As per bartleby guidelines we are supported to answer only first three subparts,  kindly repost…

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

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Q: 1 Cos(2x)dx 0. (i) Using composite Trapezoidal rule with n = 2, 4

A: As per the policy of bartleby the provisions is to solve only one question at a time So I am solving…

Q: c) Use trigonometric substitution to integrate dx 4-x2

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Q: Find the value of dy/dx at (1,0) of 2re" – In() = 4y² + 2a sin

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Q: 7T 2 Find 35 cos(7x) dx 5π 2 7T 2 35 35 cos(7x) dx = -5π လ

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Q: -6e' sin(at – 3) dt

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Q: 4. f cos? 2x 4. cos? 2x sin 2x dx 2 2 5. f sin¹¹ ²3x cos / x 3x dx

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Q: 10. J(3x3 — 5х + sin3x) dx -

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Q: 9- for y = cosx is dx a)sinx b)sin2x c)-sinx

A: As per the bartleby guideline for the multiple question it is allowed to solve first question of…

Q: (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A: Given,  ∫2xe3xdx ; We have to integrate using integration by parts ∫cosx22xdx ; We have to…

Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

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Q: – cos(4x) dx V 1+ cos(4x) d 1-

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Q: 2cosx dx Sr 1+(sinx)²

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Q: 2. Solve for general solution using exact method. (cos x cosy – cotx) dx – sinx siny dy = 0 %3D

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Q: 7T, 0 cos( {*) cos(2y)dx 2gin( gx) sin (2) dy 77

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Q: 1. S x4+a4 dx x3 2. Jydy √a2-y2 3. I cos2tdt (1+sin2t)4 4. I tanßsec2ßdß 5. [(tan) – 1)2d0

A: We have to find  the value of given intregation.

Q: Q5// Evahate dx 1- J- V&r-x 6co(3x2) dx dx sin - sinx

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Q: х2 9 dy + sinx - у %3D0 dx

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Q: 6. sin v- -2 cos Va + C %3D 4x2 1. Ja-8 dx = 18 (1-8x)4 (1-8x3)4 8. Se*dx =+ %3D In e

A: As per the instruction, we will be answering only the first three subparts. For (6),    ∫sinxxdxLet…

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

A: Integrate using substitution method.

Q: e) Differentiate f (t) = (e-6t+ sin(2-t)) -9- %3D

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Q: 1 S (4x4 – e3* + cos(2x) – + 5* ) dx - x-1

A: First you need to go through the formula of calculus. Specially go through the details of the…

Q: +3x2. Find dy/dx if: (y)² = sin5(cos³(- -)) 2 %3D

A: Given: (y)2=sin5cos3x7+3x22 ----(1) To find: dydx Let u=x7+3x22 , v=cos3u w=sin5v Now equation (1)…

Q: Find dy/dx of: x3 - sin y = (1/x3) + tan-1 (ey) - π/4 Don't simplify the final answer.

A: Given:     To determine:

Q: sin 2ydy 5.J7-3 cos 2y 15.

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Q: 2 1) (-2xy) dx + (Siny-x²) dy

A: see my solutions

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.