2. Find the area of the plane figure defined by the inequalities : x2 + y2...
2. Find the area of the plane figure defined by the inequalities : x2 + y2 <9; x2 + y2 - 6x S 0; (in the first quadrant). Use polar coordinates.
Find the area of the plane figure bounded by the inequalities : y2-x2 – 31; y s -8x – 16; y s 16x – 16.
5.Use polar coordinates system to evaluate: x2 + y2)dydx , R is the region enclosed by 0 <x< 1 and, -x sy sx
3. Let D be the region in the first quadrant lying inside the disk x2 +y2 < 4 and under the line y-v 3 x. Consider the double integral I-( y) dA. a. Write I as an iterated integral in the order drdy. b. Write I as an iterated integral in the order dydx c. Write I as an iterated integral in polar coordinates. d. Evaluate I
9. Find the area of the surface by rotating the curve y2 -1 = x; 0 < x < 3 about the X-axis.
Find the maximum and minimum of e-x2–v? (x² + 2y) on the disk x2 + y2 < 2.
Use cylindrical coordinates to calculate : x2 + y2 dVW : x² + y2 < 64, 05234 SS/(x2 + y2)dV =
Vector Calculus. Please show steps, explain, and do not use
calculator. Thank you, will thumbs up!
3. In this problem, let S be the surface defined be the equations: x2 + y2 + z2 = 1 and x2 + y2 < 1/2 (a) (1 point) Find a parametrization of S 0: DR3 where DC R2 (Hint: use spherical coordinates). (b) (2 points) Use part (a) to find the area of S. (c) (1 point) Let F: R3 R3 be the...
Let f(x,y) = exp(-x) be a probability density function over the plane. Find the probabilities: Parta)P( X2 + y2 <a), a > 0, Part b)P(x2 + y2 <a), a > 0.
3. Draw the region D and evaluate the double integral using polar coordinates. (a) SI x + y dA, x2 + y2 D= {(x, y)| x2 + y2 < 1, x + y > 1} D (b) ſ sin(x2 + y2)dA, D is in the third quadrant enclosed by m2 + y2 = 71, x2 + y2 = 27, y=x, y= V3x.