Can you please also explain how you did it? Thank you.
Can you please also explain how you did it? Thank you. i? (x, y) dA over the rectangle R - [a, b] x [c, d can Problem 1 Show that the integral be computed in terms of the numbers f(a, c), f(a, d), f...
i? (x, y) dA over the rectangle R - [a, b] x [c, d can Problem 1 Show that the integral be computed in terms of the numbers f(a, c), f(a, d), f (b, c) and f(b, d) 5 marks] i? (x, y) dA over the rectangle R - [a, b] x [c, d can Problem 1 Show that the integral be computed in terms of the numbers f(a, c), f(a, d), f (b, c) and f(b, d) 5 marks]
If f(x, y) is continuous in an open rectangle R = (a, b) x (c, d) in the xy-plane that contains the point (xo, Yo), then there exists a solution y(x) to the initial-value problem dy = f(x, y), y(xo) = yo, dx that is defined in an open interval I = (a, b) containing xo. In addition, if the partial derivative Ofjay is continuous in R, then the solution y(x) of the given equation is unique. For the initial-value...
Evaluate the double integral || f(x, y) dA over the region D. JU f(x, y) = 6x + 9y and D = {(x, y)SXS 1, x3 sy s x3 + 1}
(2) The area of the surface with equation z = f(x,y). (x,y) E D. where fra f, are continuous, is A(S) = SVGC3. y)]? + [f;(x, y)]? +T dA If you attempt to use Formula 2 to find the area of the top half of the sphere x + y2 + 2? = a, you have a slight problem because the double integral is improper. In fact, the integrand has an infinite discontinuity at every point of the boundary circle...
(1 point) Let R be the rectangle with vertices (0,0). (8,0). (8, 8), and (0,8) and let f(x, y)- /0.25ry. (a) Find reasonable upper and lower bounds for JR f dA without subdividing R. upper bound lower bound (b) Estimate JRf dA three ways: by partitioning R into four subrectangles and evaluating f at its maximum and minimum values on each subrectangle, and then by considering the average of these (over and under) estimates overestimate: Inf dA underestimate: JRfdA average:...
. (5pont)Thedale integraltegralsovertherduis an improper integ da dy is an improper integral that could be defined as the limit of double integrals over the rectangle [0,t] x [0, t] as t-1. But if we expand the integrand as a geometric series, we can express the integral as the sum of an infinite series. Show that Tl 2. (5 points) Leonhard Euler was able to find the exact sum of the series in the previous problem. In 1736 he proved that...
Someone please show how to compute the integral of b over the given region. The answer is in blue but I am not sure how to get there. 12. D = {0 <<<5,0 < < cos } (a) Sketch the region D T EEN -1 (b) Compute the integral of the function f(x, y) = sin r over the region D. NI-
Evaluate the integral [c F.dr. F(x, y) = (x + y) i + (3x - cos y) j where is the boundary of the region that is inside the square with vertices (0,0), (4,0),(4,4), (0,4) but is outside the rectangle with vertices (1, 1), (3,1),(3,2), (1,2). Assume that C is oriented so that the region R is on the left when the boundary is traversed in the direction of its orientation.
A continuous probability density function is a non-negative continuous function f with integral over its entire domain D R" equal to unity. The domain D may have any number n of dimensions. Thus Jpfdzi..d 1. The mean, also called expectation, of a function q is denoted by or E(a) and defined by J.pla f)dy...dr The same function f may also represent a density of matter or a density of electrical charges. Definition 1 The Bivariate Cauchy Probability Density Function f...
(a) Evaluate the double integral 4. (sin cos y) dy dr. Hint: You may need the formula for integration by parts (b) Show that 4r+6ry>0 for all (r,y) ER-(x,y): 1S2,-2Sysi) Use a double integral to compute the volume of the solid that lies under the graph of the function 4+6ry and above the rectangle R in the ry-plane. e) Consider the integral tan(r) log a dyd. (i) Make a neat, labelled sketch of the region R in the ry-plane over...