
Problem 3 Integrate | 14+23/4),r17A dr. Problem 4 Integrateſ esin(1) cos(2) dx.
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5) S; 5) Express the integrand as a sum of partial fractions and evaluate the integral. 7x - 10 6) S -dx x² . 44 - 12 6)
Use trig identities to rewrite the integral then integrate. 1. 2. 3. 4. 5. 6. tan(r)dr tan(r)dr (sinz + sinz + tan2)/sec2rda Sin.TS2nT (sin(2x)/cosrdr (sin(2))/1+cos2rda (cos(x) + sin(2))/sinrdr tan(r)dr tan(r)dr (sinz + sinz + tan2)/sec2rda Sin.TS2nT (sin(2x)/cosrdr (sin(2))/1+cos2rda (cos(x) + sin(2))/sinrdr
cos'x dx sin 3x dx 2. an 45 sin cos'xdx 4 sin'xcos'x dr 44 sin'x cos'r dr 6. sin'xcosx dx 8. Jo sin'x cosx dx fa-sin 2x)' dx sin x + cos x dx 10. 9 f sin'z dx cos'x sin'x d 12. 11 sin'x Vcosx dx 14. 13. cot'r sin'x dx 16. cos'x tan'xdx 15 dx sin x dx 18. 17 1-sin x cos x tan'x dx 20. tanx dx 19 sec'x d sec'x dx 22. 21 tan'x secxdx...
- 2 + 6 Integrate -dx. 23 + 3x The partial fraction decomposition is (write all terms as fractions): dx The final answer is: dx = 23 + 3x Check Answer
integrate. state du and u
a) tan(4x sec (4x)dr dx r +1 b) dx x +1 c) csc (3xax
a) tan(4x sec (4x)dr dx r +1 b) dx x +1 c) csc (3xax
1. Integrate. (a) Vr+3ds (b) x sin (x) cos (2x)dx
Use Symbolics in Matlab to integrate the following ordinary differential equation. dy/dx + y cos(2x) = (1/2) sin 3x
Integrate fc2x (2x + 4)ex2+4x–3 dx
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0
4. (a Let (sin( x cos( ) dr...
Determine the following anti-derivatives: Problem 1: S (2.² + 6x - 5) dx Problem 2: S(cos(x) - sin(x)) do Problem 3: 5 (v + + + 2 **) do Problem 4: S (3e" + ) dx