L = sa V1 + [f'(x)]?dx = Se 1 + 2 dx dx Examples. Find the length of the arc of the following curves. y = Vx3 fromx = 1 to x = 4 2. y = {(x2 + 2) from x = 0 to x = 3 3. y=*+ from x = 1 to x = 3 (Ans:*) 2x 4. y + from x = 2 to x = 4 8x2 5. y = -x2 - In x from...
question 41 and 47
41. cotx dx dx V1 – x2 sin-'x 45. Sittende 47. ( x(2x + 5)8 dx
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
Problem 1 (a). Make a sketch of the 1-form w = (l sin(x)| + 1) dx supported on U = [-r/2.2 [2 marks]
Problem 1 (a). Make a sketch of the 1-form w = (l sin(x)| + 1) dx supported on U = [-r/2.2 [2 marks]
Determine the following integrals T Sin(x) 1 + x² dx 2). xe 2x dx Idy dx + P(x) y = Q(x) integration factor Solve dy Ex dx sinx the following differenti al equations ... + 3y t? dy F) (l+x) dx +y=vx V: eSP(x) dicas
(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'
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. 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
(d) Use the Integral Inequality to prove that sin (rx(In(x + 1) dx = 1 671 (2) - In(3) - ;) 4
1. (a) Find L4 and R4 for the integral
1 (x sin x/2) dx
Show the setup and round the answer to threedecimal places.
(b) Find M4 for the integral
1 (x sin x/2) dx . Show the setup and round the answer to four
decimal places.
Sketch the approximating rectangles on the graph.
(c) Compare the estimates with the actual value
1 (x sin x/2) dx
10.243 . Which estimate is the most accurate?
(d) Express the integral from...