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
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...
please show all work and match the answer choices! thank you! 1 216 Cos 6x + <3 cos 6x dx A) 3x3 sin 6x + }x2 cos 6x - Box sin 6x- LE 2 o 1x3 cos 6x + 1x2 D. sin 6x + 2 co B) 4x3 sind sin 6x -x2 cos 6x + x sin 6x + 36 216 cos 6x + c 1 1 1 sin 6x - -X COS 6x - 36 sin 6x + 216...
13. Evaluate, S sin 5x cos x dx. Also prove that, 52" sin mx cos nx dx = 0 Using reduction formula *****
(d) Compute 2m f(x) sin(3cr)d (Hint: Recall that sin2(2nnx/a)dx = f 2(2nnx/a)dx = £] COS' (d) Compute 2m f(x) sin(3cr)d (Hint: Recall that sin2(2nnx/a)dx = f 2(2nnx/a)dx = £] COS'
Am = } $(w). cos(mkr)dx Bm= f(x) = sin(mkr)dx - Given the periodic quadratic periodic function f(x) = G) "for - <x< . Calculate Ag. There is a figure below that you should be able to see. You may (may not) need: Jup.sin(u)du = (2-u?)cos(u) +2usin(u) /v2.cos(u)du = 2ucos(u)+(u2–2)sin(u) -N2 0
Solve: ſ et cos x dx
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...
(1 point) Find the general indefinite integral S sin 2x dx. cOS X Answer.
1. a) Substitute u = sin(x) to evaluate sin^2(x) cos^3(x) dx. [trig identity sin2(x)+cos2(x) = 1]. b) Find the antiderivatives: i) sin(2x) dx ii) (cos(4x)+3x^2) dx