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

Q: Find L[et tsin(2t) - e-2t+3 +e-2t cos 3t]

A: BY USING THE LAPLACE TRANSFORMATION RULES  WE GET OPTION (D) IS CORRECT OPTION.

Q: s nip

A: Given: 12cos2x+C=14cos2x

Q: Q3:- If x= sec 0- cose and y = sec" 8- cos" 0 Prove or disprove that (x2 + 4) ) = n2G2+ 4) %3D

A:

Q: 15. Evaluate 2 (3x + cos 4x) dx

A: The given integral is: I=∫0π2 3x+cos(4x) dx

Q: 19. Evaluate the following sin³ [sin³ (2) cos(4) dx 32 A. 35 COS 5( 4 ) [-5cos² (4)+7] -cos 32 32 -…

A:

Q: n the der natwe of Sin (x )= Sin Cx-cos (rE)) to CoS

A: Definition: Differentiation is the action of computing a derivative. The derivative of a function y…

Q: What is the particular solution of the function 3e" sin 5x – cos 5x? A cos 5æ + Bsin 5x + C'e" cos…

A:

Q: Evaluate: Jcos 2xdx cos2x cos32х + C 6 A 2 sin2x sin32x + C 6 B 2

A:

Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: Evaluate: Jcos 2xdx cos2x, cos³2x + C 6 A + 2 cos 2x + C 6 cos2x B sin 2x + C 6 sin2x 2 sin2x sin32x…

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 Casx Sin"x =A +B Cos aX+C cas 4X+ Dcos Əx CoS 4X then A =[ B =1 C = %3D D.

A:

Q: Evaluate: Je*cos(7e*)cos(4e*)dx. ④ 금Sn(3e)- sin(11e")+C sin(11e*) + C 22 A © -cos(ae)- cos(11e) +c…

A: The given integral,   ∫excos7excos4exdx

Q: Stan 2xdx O-In(cos 2x) + C O-In (cos 2x) + C O-In (sin 2x) + C O tan² 2x 2 + C

A: INTEGRATION

Q: D[Expf-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: Evaluate: e* cos (7e*) cos (4e*) dx - sin (3e*) + –sin (11e*)+C A 22 B - sin (3e*) – –sin (11e*) +C…

A: Evaluation of the Integral

Q: Evaluate: / sech[in cosr Janx dx A -2 tan-1(e cosx) +c cOsx B) None 2 tan -(e cOx) + C COSA D - 2…

A:

Q: Evaluate the integral. 7/2 cos 6x dx COS -T/2

A:

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: Compute 2° sin(x" + 2) dæ. O -7 cos(x" + 2) + C O 1 cos(x² + 2) + C O - cos(2" + 2) +C 1 cos(2" + 2)…

A:

Q: Which of the following is true? cos(x) + cos(7x) ® s Ssin(4x)cos(3x)dx = [s A 2 B) All of the above…

A:

Q: Solve 2cos? (x) +3 cos (x)+1=0 for all solutíons osx<2 TT

A: Given 2cos2x+3cosx+1=00≤x≤2π

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: Evaluate: Je* cos (7e*)cos (4e*) dx ® -co (3*) -cos (11e') + C -(-*)* sin (3e“) –sin (11e*) +c A 22…

A: The given integral,       ∫excos7excos4exdx

Q: Evaluate cos (x (x2 – 2x + 1) (2x - 2) sin (x 2 - 2x +1) (2 – 2x) sin (x? – 2x + 1) O (2x 2) cos (x-…

A:

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y (π/8) = 0…

A: Given,y(x) = C1 sin2x + C2 cos2x + 1 — (1)Here we find the value of C1 and C2 such that the equation…

Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

A:

Q: ,2 Compute x² cos(x³ + 3) dx

A:

Q: COs 05

A:

Q: 18. Evaluate fe³x cos 8x dx e3x a. [8sin 8x 3 cos 8x] + C 3x b. [8sin 8x + 3 cos 8x] + C 73 C. d.…

A:

Q: 28. Evaluate f 5 sin 3x dx 2+cos 3x a. 2 In 15 sin 3x| + C b.- In 12+cos 3x|+C c. In 15 sin 3x| + C…

A: Evaluate integral

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

A:

Q: Which of the following is true? A Jcos(3x)cos(4x)ax = [ cos(x) + cos(7x), 2 ® Jsin(3x)sin(4x)dx = […

A:

Q: Evaluate f(e' + cos(30) de 1 [ (x³ + cos(3.x)) dxr x sin (3x) ,. a) 4 r* sin (3x) b) 4 3 3 x* sin…

A:

Q: Evaluate: Scos 2xdx cos2x, cos 2x +C A 2 6 sin2x sin32x +C 6. B 2 cos2x cos 2x + C 6. 2 sin2x,…

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: 3Tt of cSC X du If u = f(x), then dx cos X . Compute %3D 2 sin x и -

A: Given ,  u = f(x)

Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

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: F.(3e-3 sin(2x')) is equal to 2 3. n 4+@² 3 cos 8 4 3. 7(1+o² 4 cos 4 4 1 3, 1 +4cos 4. 4 2 1+@ 4…

A: Use the following formulas to calculate the Fourier cosine transform. Fee-ax=2πaa2+ω2…

Q: Given: cos 3y + sin 2x 2 cos 2x 2 O -3 sin 3y-3 -2 cos 22-2 O -3 sin 3y 3 O -2 cos 2x-2 3 sin 3y 3 2…

A: Given: cos3y+sin2x=2x+3y To find dydx in the given equation.

Q: Find 2 if x? cos4 cos* T. 1) 2xcos x+4x2cos3xsinx 2) 2xcos x- 4x²cos³xsinx O3) 2xsinx sin xcosx 4)…

A: Hence option (2) is correct.

Q: Evaluate: Je*cos(7e*)cos(4e*)dx. 1 A 1 ④ 능Sin(3e")- Sin(11e") +C sin(11e*) + C 22 1 (в 1 sin(3e*) +…

A:

Q: Evaluate: Jx°cos(2x)dx A None of the given choices 2x2sin(2x) +2xcos(2x) + sin(2x) + C 4…

A: I have used the by parts rule of integration and get the required integral . Option (D) is correct.

Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 01 + tan 02 + tan 03 + ... + tan 0,} =…

A:

Q: Evaluate: Je*cos(7e*)cos(4e*)dx. 1 - cos(3e") - -cos(11e*) +C 22 sin(3e") - sin(11e*) + c 22…

A:

Q: 4) Find when y2 – x² + cos(x + y) = 0

A:

Q: b) 4 (€) -et cos (dt+물) cos (2dt +물) COS 3

A:

Q: Question 6 Compute the following integral: sin (8z) de 1 4 a) cos(8x) sin*(8x) + C 32 1 cos (8r) + C…

A:

Q: Suppose f (x) =cos( 2– 3x). Evaluate: )dx A - 3sin(3x – 2) +C ® -;sin(3x – 2) + C sin(3x – 2) + C D…

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.