2a + acoth 2z ) dz \sin 3z a/2

Q: Evaluate the integral. .5 3 cosh(t) dt 0.

A: Solution

Q: 2. Use Cauchy's Integral formula, Evaluate the following sin42 IZ1= 3. (Z-4)3

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

Q: To evaluate the integral 1. 7 64 + x² -dx,

A:

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

A:

Q: Find the indefinite integral: 10sin 3x - 15 cos 2x + 6 e5x + C O 90sin 3x -60 cos 2x + 150 e5x + C…

A: 30∫cos3x+sin2x+e5xdx=30· ∫cos3xdx+∫sin2xdx+∫ e5xdx=30·…

Q: The integration expression Jsin(3In(x)+ 4)cos(3In(x) + 4)dx must be transformed into using suitable…

A:

Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

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

Q: Evaluate the integral: 25 tan² 12x dx Choose the most appropriate answer. tan3 3 12x O 25 × 1 12 ln…

A: Explanation of the answer is as follows

Q: 5. Show that dS = 0. lav

A: The objective is to show that, ∮∂VdS=0. Let V=cT where c is a constant vector. Now by divergence…

Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: Evaluate the integral  ∫(7(1-tan^2(x)/sec^2(x)) dx

A: We have to evaluate ∫71-tan2(x)sec2(x) dx

Q: Find the area.   y = 3 cos(4x),    y = 3 − 3 cos(4x),    0 ≤ x ≤ π/4

A:

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

A:

Q: Find the indefinite integral: O 10sin 3x - 20 cos 2x +6 e5x + C 90sin 3x 60 cos 2x + 150 e5x + C…

A: The objective is to find the indefinite integral.

Q: The integration expression sin(3In(x) + 4)cos(3In(x)+ 4)dx must be transformed into using suitable…

A: topic- indefinite integration

Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: The integration expression sin(3In(x) + 4)cos(3ln(x) + 4)dx must be transformed into using suitable…

A:

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

A: Consider the integral

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π.…

A: Consider the given function y=4cos0.5x

Q: 6) Prove mathematically that (1 grad = 0.9 deg) %3D

A: Since, this is a multiple question according to the Bartleby Answering rule, only first question is…

Q: Evaluate the integral S cos ³ x + 8 sin x cos³² x + 6s in ² x dx; cosx #0 2 cos²x

A:

Q: sin 3xdx Evaluate: S 4+cos?3x

A:

Q: This is exercise 12 of Section 7.5 page 460. Find the integral sin(2x) dx +C 1+ sin (x)

A:

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: 4. y = √esinx + 2 5. y = 4x In 4x 6. xe = sin 5x - sin 3y

A:

Q: Use the results of Section 5.2 to compute the following definite integral: 4x2 dx %3D

A:

Q: 2. Apply appropriate trigonometric substitution to compute the integral 1-4x +2 dx /2x

A:

Q: can this be evalnated by using L'HUSpital's Rule? im x2 3x+ 2 sin(x x)

A:

Q: What substitution should be used to solve the integral O sinu=3x/2 O sec u =2x/3 O sec u =3x/2 O tan…

A:

Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

A: Since you have asked for a question with multiple sub-parts , we will solve the first three…

Q: The integral of tan^2 (x) sec^4 (x) dx

A: To determine the given trigonometric  integral.

Q: Evaluate the Integral |4sin²0+4 sin 0 5. S de tan²0+1 ANSWER: 5. - [(2 sin 0 + 1)V4sin²0 + 4 sin 0 –…

A:

Q: S cos (2x) sin* (2x)dx a.

A: Solution: The objective is to evaluate the integral

Q: What is the integrable form of sin-cos-sin0 de 2 2 du 2 1– u² du cosu du -2 sinu du

A: To write the integrable form.

Q: The answer of integ ra Ssinzx cos3% dX

A: We have to evaluate the given integral.

Q: Find S(3/(x) + cos7x + 4 + 20) dx None x1.5 sin7x + 4log x + 20

A: Now,  We will find the integration to the given problems.    Integration of cosec2x dx = - cot x +c

Q: 2* csch (2*) cosh(2*)-sinh(2*)

A:

Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

A:

Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

A:

Q: Evaluate the integrals ( sec5 3x tan 3x dx

A:

Q: In (xle)secx (2- sec²x) ha sec(3A – x) Ju"du? What should be the value of A for dr to be integrable…

A: Note -  Acc. to Bartleby guidelines, we are supposed to do only one question . If you want more to…

Q: 8. S(1- sec3x)²dx

A:

Q: 2 = sin5t constitute a fundamenta L

A: Y1=cos5t and y2=sin5t  do not a fundamental set of solutions of differential equations y"+16y=0

Q: Compute the integral S do 2-sin 0 *

A: Apply linearity: Apply tangent half-angle substitution:

Q: 39.) Show how to use (a) trapezoidal rule and (b) Simpsons rule with n=4 to 4 approximate ſ,"…

A: There are different methods of solving a definite integral without integrating it such as the…

Q: Find the definite integral of ³ Option 1: 4 Option 2: Option 3: Option 4: Option 1 Option 2 Option 3…

A:

Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: 3-Expand In [x? sin³ x /vx2 +1]

A:

Q: Prove that 1- cosh -1 x= In(x+ Vx- -1 1 x+1 2- coth -In x-1 X = - Vi+x? .2 1 3- csch -1 x = In(-+

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.