K The vibrating string problem is given by the equations below. Solve this problem with a = 3, L= x, and the initial functions f(x) = 3 sin 4x + 2 sin 7x and g(x)= 14 sin 9x-10 sin 12x au u(x,t) = =² 2² u(0,t) = 0 u(L,t) = 0 2u ax 00 tz0 t20 u(x,0) = f(x) ди (x,0) = g(x) 0≤x≤L 0≤x≤L CEED

Q: (b) sinr + cos² y 4 P(품,등) 3

A:

Q: 2π 6 11. 3r2 sin e drd0 0 0

A:

Q: x= 4 sin t - 4, y = 4 cos t -3 Eliminate the parameter t

A: we can eliminate 't' . sin2 t + cos2t =1

Q: S d.x √9-4x²

A:

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 2) [sen² (x) cosª (x) dx

A: The given integral is         I =  ∫ sen2(x)cos4(x)dx           =  ∫ {1 - cos2(x)}cos4(x)dx…

Q: A = (a) Find cos(At) and sin(At) -2 3 (b) Find the general solution of y" + a²y = 0 where a ‡ 0

A:

Q: 2 (x + 3π)]dx

A:

Q: 3. cos y sin 2x dx + (cos² y – cos² x)dy = 0

A:

Q: 2 cos @ dӨ . 1- sin 0

A:

Q: ۱/۱ solve b find dy dx y = X √ Sin³ (x+1) cos (x²+1) 3/1+2 Ln (x+1) 2 -1 Find Value of Sin (x) - tan…

A: 1)2)

Q: S(csc x cot a + 8x7)dx csc x x8 + c - cs x x8 + c - - - csc x + x8 + c - csc x + x8 + c O cot a + 8…

A:

Q: 1– sin (t) 1 2 sec? (t) = + cos² (t) `1-sin (t)

A: To verify 2sec2t=1-sintcos2t+11-sint

Q: Q6// find the general solution (sin-ix+- 1 dx + sin-1xdy 0

A: Note the following result of integration. We will use it in the solution :

Q: Solve the ODE: (3e3 sin y-42y sin(7x)) dx + (e³ cos y + 12y cos(7x)) dy = 0 Entry format: Write your…

A:

Q: sin?(Væ) + cos (V)) dA, where R= [0, 2] × [0, 2]. R

A: The given integral is: I=∫∫R sin2x+cos2y dA,       where R=0, 2×0, 2

Q: 2 L-1 (s+2)²+3 бе 6e-2t sin3ta O 2e-2t sin/3t0 .b V3et sin 3tco 2/3e-21 sin/3t.a0

A:

Q: TT/2 S,"/e cos?x.sint x dx in tegralinin bulunvz sonucunu

A:

Q: Exercise III (a) Let I = psin(ø) cos (0); y = p sin(6) sin(0); pcos(6). Then find the following. (i)…

A:

Q: TL (3x −2+ sinx) dx

A: The given integral,         ∫-π4-π23x-1x2+sinxdx

Q: a csc 0 /2 co π/4 Jπ/40 p³ sin²0 sin o dp de do

A:

Q: f(x) A B = arcsin x, then lim 1/1/12 0 ㅠ 6 f(x)−ƒ( ² ) X→ X- 1|2 is

A:

Q: Find if dy y = e2 sin x Choose the correct answer.

A:

Q: step by step

A:

Q: dx x4+16 Įtan-( x2 + c 4

A: Given that, ∫xx4+16dx

Q: A. Eliminate the arbitrary constants of y = C₁ sin 2x + C₂ cos 2x + 3x². B. Prove that (y-2)(x - 1)…

A:

Q: 5а. (inverse trig functions) 5b. 10 V49 – 25x? sec x (100+sin? x)

A: Given, ∫549-25x2dx    and  ∫10secx·10+sin2xdxwe have to solve this

Q: 8 csc? 4x cos(cot(4x)) dx sin² (cot(4x))

A: Here, I will be using method of substitution to solve this integral. You can assume:…

Q: We know that [e³x sin(2x)dx= =e³x (3 sin(2x) - 2 cos(2x)) + C Find a a=1 201 3903 27 ~ tv 8 0 W

A:

Q: Find the first two positive solutions to 2 sin(3t) 1 t -

A: We have to find first two positive solutions to given equation.

Q: 8 cos5(α)/(sin(α))1/2 dα

A: