



4. Integration: TT (a) Si Jachtvoz dx (b) sin x dx (6-cos x)3 (c) , (2-2)'...
TT 4. (9 points each) Integration: (a) Si vachtvasz dx (b) Số 6 cos x) sinx dx 26-2)' ()dx (d) St(t – 5)8dt (e) 56x?=***V7-4 dx
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TT 4. (9 points each) Integration: dx (a) si veci+V*2 sinx (b) S2 dx (6-cos x)3 (©) 1.6-2) ()dx (d) St(t – 5)8dt 56x?**** 6x7-x*+Vx-4 dx
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4. (9 points each) Integration: 77 1 Vx(1+x)2 sinx (b) S3 -dx (6-cos x) 3 (© 1.6.-2) )dx (d) St(t – 5)ºdt (e) 56x?=+*+VX-4 dx
Q1 dx, 115 5xita dx. 2) ſ tan°4x dx . 3) 06-341 S[cos(x? 4) + 1) + xdx, 5) prove that I cscu du = -Inlcscu + cotul + c x2 + Q2 r3 dx 1) dx 2) sino cosºede , 3) /* sec°8 de , 4) * sec`e do , 4) , Port + 4 1 5) dx . 4- x2) 4 Q3 Answer A or B (graph the functions) A-Determine the area of the region enclosed by y...
ENG 1005 ASSIGNMENTI QUESTIONS (1) Use integration by parts to calculate sin(In(x) dx and Here, In is the natural logarithm. cos(In(x))dx. [5 marks (2) (a) Use integration by parts on sinh(t) sinh(t)dt and the identity cosh (1) = 1+sinh'in to calculate the integral of sinh(r). (b) Calculate the integral of sinh(r) by expanding the product and then integrating, Confirm that you get the same answer as in part (a). (e) Show that if x is a positive real number, then...
Evaluate the integral 1 ET sin(2²) dx dy by reversing the order of integration. With order reversed, 6 sin(x²) dy dx, where a = ,b= C= and d Evaluating the integral, So S, sin(x2) dx dy =
Find the derivative of each
one.
a. y = (tan(x2 + 1))4 + 5 In Vx b. с. У-(sin x)cos x
a. y = (tan(x2 + 1))4 + 5 In Vx b. с. У-(sin x)cos x
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) - (sin t, cos t, sin 2t), 0 s t s 27. (Hint: Observe that C lies on the surface z - 2xy.) F dr-
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) -...
4. Use integration by parts to evaluate the following integrals. (a) [(x +3) (x+3) sin(2.c) d.c (2.5 - - 1)e" dx In (2.c) d.
Supposez1 =4 cos 3 +isin 3 andz2 =2 cos 6 +isin 6 .
Computez1z2.
(a) 8(cos?π?+isin?π?) 22
(b) 4(cos?4π?+isin?4π?) 66
(c) 2(cos?π?+isin?π?) 66
(d) cos(π)+isin(π)
(e) 8(cos?π?+isin?π?)
66
17. Suppose z1 = 4 (cos (1) + i sin (5)) and z2 = 2 (cos () + i sin (7)). Compute z122. (a) 8(cos (7) + i sin (7)) (b) 4(cos (4) + i sin (*)) (c) 2(cos (7) + i sin ()) (d) cos(T) + i sin(TT) (e) 8(cos (7)...