6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

Q: 10. Show that 2" + 42' + 8z = 0 if z = e-2=(sin 2x + cos 2x).

A:

Q: 7. Prove: sin(t) dt sin(1) + cos(1) 4

A:

Q: 7/4 Q6// S*x cos3 2x sin* 2x dx

A: we have,

Q: 2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

A: W(π/4) = -sin(π/2) = -1 W(π/6) = -sin(π/3) = - √3/2 Since, Wronskian is not zero for a single value…

Q: 11. Evaluate the integral: tan 2x dx A. -In| sec 21| + C -sec² 2x + C С. -In| cos 24| + C D. 2 sec…

A:

Q: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

A:

Q: B\ Suppose that = 4 cos? t , x = v3 sin(2t) and 0 < t < n. S d²y *= - tan(2t) and = -sec (2t). 1 dt2…

A:

Q: If x = sec e - cos e and y = sec" 8- cos"0 (x² + 4) (* - n°(y² + 4) = n²(v² + 4) Prove or disprove…

A:

Q: 1 If z = 2x2 – 3y with u = x² sin y and v = 2y cos x, determine expressions %3D az dz for and du

A:

Q: Q#( 1b Compute: [cos (10x)sin²(10x)dx 1 sin°(10x) – A) 30 1 sin°(10x)+C 50 1 cos°(10x)- 1 -cos…

A: We have to solve the given indefinite integral

Q: If xty= 2e Cos Øand x-y=2ies.m Ø show that Su

A:

Q: リ=!-Cos2x 1+(os 2x prove y = 2 tanx .secx

A:

Q: What values of x in the interval [0,2pi] satisfy 2 + 2cos(x) - sin2 (x) = 0

A:

Q: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

A:

Q: 1- d/dz [cosz] = -sin z

A:

Q: What substitution should be used to solve the integral x²dx |4+9x² O sin u=3x/2 sec u =2x/3 O sec u…

A:

Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

A:

Q: 8. -dt 1+64t 2 sin-8 B. А. (). -1 2 tan 2 tan- 8 O c. D.

A:

Q: Prove | cosz |2 = cos²x+ sinh²y.

A: To Prove: cos z2=cos2x+sinh2y

Q: Evaluate: 8 sin xcos xcos 2.xdx -cos 2x- 1 cos 2x +C 10 8 cos 2x--cos 2x +C С. A. 14 1 -cos 2x 10 1…

A: Integration is generally used to calculate area under the curve. When function definition changes…

Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

Q: 7) {(1- sin° 31)- cos3t dt 8) | t in’ (5x)· sec´ (5x) dx

A: 7) I=∫1-sin2 3t·cos 3t dt  ……1

Q: Which of the following is true? O Scos(3x)cos(4x)dx= [ r cos(x) + cos(7x) dx B Jsin(3x)cos(4x)dx= […

A: Option D

Q: S cos(3z)sin1º(3z) dz C 1 (cos (3z))10 + C 3. (sin(3z))10 + C D 1 (cos (3z))1 + C 33 (sin(3z))'l + C…

A: Topic = Integration

Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: S cos(3r)(sin(3x) +5)10 dz Select one: (sin(3z)+5)" 11 +C O (sin(3r) + 5)"+C (sin(37)+5)" 33 +C…

A: Consider the integral: I=∫cos3xsin3x+510dx……1

Q: Which of the following is true? ® Ssin(3x)cos(4x)ax =S sih(7x)= sin(x) A 2 ® Jsin(4x)cos(3x)ax = […

A:

Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

A:

Q: If x= cos n + cos 2n and y=sin n + sin 2n show that  2xy= sin 2n+2sin 3n+sin 4n

A: See the attachment

Q: Which of the following is true? @ Jcos(3x)cos(4x)dx= [ cos(x) + cos(7x) 2 BAll of the above ©…

A:

Q: [0; 2n) v3 sen x+ COS X 16

A:

Q: Evaluate the integral. sin (8t + 16) dt cos (8t + 16) sin (8t + 16) dt = cos (8t + 16)

A: Solved below

Q: Find dy if y= 5x² sin4x dr O None -20x? cos4x – 10xsin4x 20x² cos4x + 10xsin4x O 10x² cos4x +…

A: We apply u*v rule of derivatives d/dx (u*v) = v*du/dx + u *dv/dx

Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=

A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…

Q: Find L{10) } s(s²+16) 1+cos(4t) 16 1-cos(4t) 4. 1-cos(4t) 16 1+sin(4t) 4 1-sin(4t) 16

A:

Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

A:

Q: The suitable substitution to evaluate the integral cos°(2x) dx is 5(2x) 3 csc°(2x) u = sin(2x) u =…

A: First, simplify the integrand and use the substitution method

Q: Which of the following is true? J sin(3x)sin(4x)dx = cos(x) – cos(7x) dx 2 ® Jsin(3x)cos(4x)dx = […

A:

Q: 7) Evaluate the indefinite integral / cos cos 2t sin 2t dt.

A:

Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: The answer of integ ra Ssinzx cos3% dX

A: We have to evaluate the given integral.

Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

A:

Q: Which of the following is true? A Jsin(3x)cos(4x)dx= [ Sin(7x) – sin(x) Jcos(3x)cos(4x)dx= [cos(x) +…

A:

Q: Find , if da y = 3x cos4x 12x* sin4x – 10x cos4x None -2x4sin4x – 12x° cos4x -12x4 sin4x + 12x°…

A:

Q: Compute cos² x dæ. cos 2x +C 4 cos 2x +C 4 2 sin 2x +C 4 2 O cos cos x +C 3 +

A: Formulae:

Q: 6. S cos 4x cosx dx will yield B.금sin Sx + 등sin 3x +c А. sin 5x + sin 3x + C c. 글cos 5x-글cos 3x + C…

A: Note: As per company policy we should solve only one question. So kindly repost the other questions…

Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

A:

Q: Show that 1 − cos x = x2/2 with an error less than 0.003 for |x| &lt; 1/2.

A: Given: 1-cos x =x22;    |error|&lt;0.003Formula:  The…

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.