13. Evaluate, S sin 5x cos x dx. Also prove that, 52" sin mx cos nx...
Using reduction formula ***** 13. Evaluate, S sin 5x cos x dx. Also prove that, 53.4 sin mx cos nx dx = 0
Use the substitution formula to evaluate the integral. 1/2 COS X s dx (5+5 sin x) 0 3 OA 1000 OB 3 200 OC. 3 200 OD. 12 125
Entered Answer Preview – 3x (-3/34) *[e^(-3*x)]*sin(5*x)-(5/34)*[e^(-3*x)]*cos(5*x) gåe-3* sin(5x) – 5 34 e cos(5x) (1 point) Find the integral. |e** sin(5x)dx = (-3/34/E^(-3)sin(52)-(6/34/e^(-3x]cos(52)
Evaluate the following integral. 1/2 7 sin ?x -dx 1 + cos x 0 1/2 7 sin 2x dx = V1 + cos x 0 Score: 0 of 1 pt 1 of 10 (0 complete) HW Score: 0%, 0 of 10 pts 8.7.1 A Question Help The integral in this exercise converges. Evaluate the integral without using a table. dx x +49 0 dx X2 +49 (Type an exact answer, using a as needed.) 0
13. Evaluate: (emcos x dx. Hint: Notice we see sin x and its derivative cosx. u=sin x is a good choice for substitution. 14. Evaluated as 15. Evaluate: x cos(x") sin(x)dx. Hint: Since the cosine function is taken to the 4n power, try u = cos(x).
use residue theorem to evaluate the following integrals sin z 21) 20) Cosx dx (r? + 1) X 22) sin mx dx 2(x² + a²² (a > 0, b>0) 23) cos ex - cos bx -dx x?
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
3. Let W (x, t) = (coswt)(a cos nx+b sin nx) and (x, t) = (exp -kn-t)(a cos nx+ bsin nx). Here n is a positive integer, 2,t are real variables, and a, b,w, k are real constants with k positive. a. Evaluate W(x,0), H (2,0) and əW/ət(x,0) for all c. b. Show OH/ət = k(32H/8x2) for all x,t. c. Find some positive constant c so that w2w/at2 = c(32W/8x?) for all x, t.
*Prove that the orthogonal systems {sin nx)., and {ï, cos nxml are both complete on [0, T] 3.
Evaluate the integral. (Use C for the constant of integration.) (4² + 5x) cos(x) dx Show My Work (Required)