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4. Integration: TT (a) Si Jachtvoz dx (b) sin x dx (6-cos x)3 (c) , (2-2)' (3) dx (d) St(t - 5)8dt 6x7-x*+VX-4 dx x2
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 1 1 pts If f(x)dx = 10 and Să f(x) = 3.6, find si f(x)dx. 6.4 Question 2 1 pts Let Só f(x)dx = 6, Sº f(x)dx = -4, So g(x)dx = 12, S g(x)dx = 9 Use these values to evaluate the given definite integral: Si (35(x) + 2g(x))dx —
If Si f(x)da = 12 and so f(x) = 2.8, find si f(x)dx. Question 2 1 pts Let f(x)dx = 6, S. 8(x)dx = -4, S g(x)da = 12, g(x)dx = 9 Use these values to evaluate the given definite integral: (+1) da
4. If si f(x)dx = 10 and si g(x)dx = 6, then [2f(x) – 39(x)]dx is
If f is continuous and 6". 16 f(x) dx = 12, find Lox xf(x2) dx.
In Problems 3-6, find the critical point set for the given system. dx 4. dx = x-y, 3. dt y1 dt dy dy = x2 y2 - 1 dt = x + y + 5 dt dx dx x2- 2xy y2- 3y 2 6. 5. dt dt dy dy 3xy - y2 (x- 1)(y 2) dt dt
3. Find x2 dx if it exists VI+x3 2
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
Question 2 please
1 and 2, determine whether or not the integral is In exercises improper. If it is improper, explain why 12. (a) 12 x-2/5 dx 「x-2/5 dx 「x2/5 dx (b) (c) I. (a) 0 13. (a 40 1 dx 2 x 14. (a In exercises 3-18, determine whether the integral converges or diverges. Find the value of the integral if it converges. 15. (a (b)人1x-4/3 dr 3, (a) l.lyMdx (b) x43 dx 16. (a 4. (a) 45 dx...