Question 11 3 pts Compute the line integral forma sin z ds, where is the curve in R3 with parametric equation r(t) = costi+ sintj+tk, 0 <t< /2. The value of the integral is So x2 sin z ds = 1
20. (4 pts.) Compute the indefinite integral of S x(3 + 5x2)21 dx.
1. Let P(x) = 22020 – 3:2019 + 22 -3. (b) Compute the contour integral Scof(z)dz with f(z) := 2 fled with f(-) -- 2021 – 222020+2 P2) +, where C (0) is the circle 121 = 8 with positive orientation.
Complex Analysis
1. Let γ is a positively oriented circle centered at the origin with radius r r > 0 ecos(e2) +21)9 (a) For r £ {1,2}, compute the integral .Дег+1)(2+2)3 d (b) For r and 2, find the principal value of that integral, if it exists.
1. Let γ is a positively oriented circle centered at the origin with radius r r > 0 ecos(e2) +21)9 (a) For r £ {1,2}, compute the integral .Дег+1)(2+2)3 d (b) For r...
Problem 3-21 (Algorithmic) For the standard normal random variable z, compute the following probabilities (if required, round your answers to four decimal places): P (0 ≤ z ≤ 0.88) = P (-1.51 ≤ z ≤ 0) = P (z > 0.43) = P (z ≥ -0.24) = P (z < 1.80) = P (z ≤ -0.78) =
4 : a) (10 pts.) Compute the triple integral z dzdydz where D is the circular cone described by, with h, a positive constants. b) (10 pts.) Compute the surface area of the cone from part (a). y)
-/5 POINTS Compute the surface integral of the function f(x, y, z) = 3xy over the portion of the plane 4x + 3y +z - 12 that lies in the first octant. Submit Answer
Compute the exact value of the definite integral Z 5 1 x + 1 x dx. simplify your answer.
Sketch the region enclosed by the curves and compute its area as
an integral along the x- or y- axis.
Sketch the region enclosed by the curves and compute its area as an integral along the e- or y-axis. (a) 1 = \y, r = 1 - \yl. (b) 1 = 2y, 2 + 1 = (y - 1)2 21 c) y = cos.r, y = cos 2.c, I=0,2 = 3
#3 Consider the vector field F- Mi+ Nj Pk defined by: F- ysinzi+sinjry cos z k. Compute the line integral ScF dr over a unit circle. Compute the line integral ysin z dr+ r sin z dy + ry cos zdz (0,0,0) #3 Use Green's Theorem to evaluate the line integral along the given positively orientated curve C. e2*t d e" dy, C is the triangle with vertices (0,0), (1,0), and (1,1)
#3 Consider the vector field F- Mi+ Nj...