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2 dx 19+x2 2 2 dac 2 х...
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but...
EXAMPLE 2 Find sin$(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...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk,...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
Question 14 7 pts Consider the line integral F. dr where REC IND РІ. F(x, y,...
Question 14 7 pts Consider the line integral F. dr where REC IND РІ. F(x, y, z) = i + (x+yz)j + (xy – z)k and C is the boundary of the plane 2 + y + z = 4 in the first octant, oriented in the counterclockwise direction when viewed from above. the following double integrals is equivalent to this line Using Stokes' Theorem, which integral? °6964 (3 - 2z+1) du dz (2x + y) dy da Question 12...
1. a) Substitute u = sin(x) to evaluate sin^2(x) cos^3(x) dx. [trig identity sin2(x)+cos2(x) = 1]....
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
cos'x dx sin 3x dx 2. an 45 sin cos'xdx 4 sin'xcos'x dr 44 sin'x cos'r...
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...
Question 11 Give the form of a particular solution of (4) – 16y-2 e 2x+3e" +...
Question 11 Give the form of a particular solution of (4) – 16y-2 e 2x+3e" + cos2x) – 1 a) z-Axe* + Be **+Ccos(2x) + sin(2x) + E d) Axe 2+Be+Cx cos(2x) +Dx sin(2x) +B 3-Axe* +Be+3+ Cx cos(2x) +Dx sin(2x) + E 2=Axe 2+36-3x+cos(2x) + sin(2x) -Ae 2*+Be9*+ C'x cos(2x) + DX sin(2x) + E None of the above. e) f) Question 12 Give the form of a particular solution of J14) - 4 7 " +13 y" –...
1. (5 points) Find the area of the region enclosed by a parabola y x2 -...
1. (5 points) Find the area of the region enclosed by a parabola y x2 - 4x - 5 and a line y = x-5. To get full credit, you must draw a picture of the problem first, then find the upper and lower bounds before finding the area. (2 42 points each) Use appropriate logarithmic properties to make the following equation easy to dy or you differentiate. Find (dx and use trig identities to simplify to the simplest answer...
10. (26pts) Find each of the definite integrals, indefinite integrals, and derivatives. 2 dx .22 5)...
10. (26pts) Find each of the definite integrals, indefinite integrals, and derivatives. 2 dx .22 5) / see?zda (7 - cos x) dc (d) dc sin (x2 – 4) dt (e) ["47" (3+z")" dx () /22"/+ 2 du
Q1 dx, 115 5xita dx. 2) ſ tan°4x dx . 3) 06-341 S[cos(x? 4) + 1)...
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...
The correct answer is shown, Im just confused about how to get there. b g(b) Use...
The correct answer is shown, Im just confused about how to get
there.
b g(b) Use the Substitution Formula, ſr9(x)) • g'(x) dx= f(u) du where g(x) = u, to evaluate the following integral. g(a) 2x 3 3 tan х dx 2x 3 S 3 tandx = 12 In 2 - 6 In 3 0 (Type an exact answer.)
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...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
Question 14 7 pts Consider the line integral F. dr where REC IND РІ. F(x, y, z) = i + (x+yz)j + (xy – z)k and C is the boundary of the plane 2 + y + z = 4 in the first octant, oriented in the counterclockwise direction when viewed from above. the following double integrals is equivalent to this line Using Stokes' Theorem, which integral? °6964 (3 - 2z+1) du dz (2x + y) dy da Question 12...
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...
Question 11 Give the form of a particular solution of (4) – 16y-2 e 2x+3e" + cos2x) – 1 a) z-Axe* + Be **+Ccos(2x) + sin(2x) + E d) Axe 2+Be+Cx cos(2x) +Dx sin(2x) +B 3-Axe* +Be+3+ Cx cos(2x) +Dx sin(2x) + E 2=Axe 2+36-3x+cos(2x) + sin(2x) -Ae 2*+Be9*+ C'x cos(2x) + DX sin(2x) + E None of the above. e) f) Question 12 Give the form of a particular solution of J14) - 4 7 " +13 y" –...
1. (5 points) Find the area of the region enclosed by a parabola y x2 - 4x - 5 and a line y = x-5. To get full credit, you must draw a picture of the problem first, then find the upper and lower bounds before finding the area. (2 42 points each) Use appropriate logarithmic properties to make the following equation easy to dy or you differentiate. Find (dx and use trig identities to simplify to the simplest answer...
10. (26pts) Find each of the definite integrals, indefinite integrals, and derivatives. 2 dx .22 5) / see?zda (7 - cos x) dc (d) dc sin (x2 – 4) dt (e) ["47" (3+z")" dx () /22"/+ 2 du
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...
The correct answer is shown, Im just confused about how to get
there.
b g(b) Use the Substitution Formula, ſr9(x)) • g'(x) dx= f(u) du where g(x) = u, to evaluate the following integral. g(a) 2x 3 3 tan х dx 2x 3 S 3 tandx = 12 In 2 - 6 In 3 0 (Type an exact answer.)
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