Find the area of the region enclosed by the curves y = x² and y = x by integrating with respect to y. (1,1) y = 1x NOTE: Enter the exact answer as an improper fraction if necessary. A = y = x²

Q: Find the approximate area under the curve of f (x) =x+1 from x = 0 to x = 2, using 4 left-endpoint…

A:

Q: 1. Sket dh the graph of the cylinder r = (y – 2)2 in R. %3D

A:

Q: Evaluate the double integral over the rectangular region 4(a sin(y) – y sin(æ)) dA; R= {(x,y) : 0 <…

A:

Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = TT, using 4…

A: Here, the interval [0,π] is divided into 4 intervals of the length of each interval is ∆x=π-04=π4.…

Q: 324-y' y dx dy 18

A:

Q: Use a double integral to find the volume under the plane z = 32x + y and over the rectangle R = {(x,…

A:

Q: What is the closed-form expression for the series 2 (k+ 1)², k=1 13 n3 + B

A: First expand the squre  term and make it in standard format then use the formula of summation.

Q: Solve the following differenti- d'y 3. +2y=e"; dx dx

A:

Q: Evaluate the iterated integral. J. J, J vz dx dz dy A 45 в) 34 (© 47/3 D) 5

A: Topic = Integration

Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

A:

Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: Let's find.

Q: Find fr(t) u(t)] and fr(t) x u(t)] in two different ways. r(t) = cos ti + sin tj + tk, u(t) = j + tk…

A: Vector

Q: The integral TT tan x sec?x dx O none of them is an impróper integral of type I that diverges is an…

A:

Q: 4 – X - 2 2 sin(x) |dx V 1 + x

A:

Q: Let R be the region shown in the accompanying figure. Fill in the missing limits of integration. y =…

A: Let's find.

Q: A shelter rescues 4 cats for every 5 dogs. If they rescued 48 cats how many dogs did they rescue?

A:

Q: Evaluate the integral. NOTE: Enter the exact answer. xe* dy dr =

A: the integration of the double integral is xexy.

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 5, 5) %3D…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point.   f(x, y) =…

Q: Perform the indicated operation. Simplify if possible. b2 64 b+8 b+8

A: To simplify the given expression.

Q: Question 6 Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 A) 6 B) 9…

A:

Q: Evaluate the triple integral. /I| ry sin(yz) dV, G where G is the rectangular box defined by the…

A:

Q: Find the approximate area under the curve of f (x) = x< +1 from x = 0 to x = 2, using 4…

A:

Q: Assume the cubic function f(z) = ar+ b +cz+d, %3D has a relative maximum value of 3 at z =-2 and a…

A:

Q: Evaluate the iterated integral. yz dx dz dy 45 в) 34 47/3 D) 5

A:

Q: Find the equation of the line perpendicular to through (7, 2) through (-1,7/2) through (1/3, 13)…

A: The line perpendicular toa) 2y-3x=1 through 7,2b) 9x+15y+6=0 through -1,72c) x+y=1 through 13,13…

Q: Express the area of the given surface as an iterated double integral, and then find the surface…

A: We have to find the surface area.

Q: Question 8 sine 1/2 I r cos e dr de. Evaluate the iterated integrals J. (A) 1/6 (в) 1/2 (D 11/9

A:

Q: Find the arc length of the parametric curve. x = e', y = et, z = V2t; 0<t< 4 L = 54.6

A:

Q: Find V· (V × F), if F(x, y, z) = 7e*²i+ 6xe"j –- 6e²k. V·(V × F)

A:

Q: 1-sin8 Evaluate the iterated integrals r2 cose dr de A 1 B) 2 D) 3

A:

Q: If 0 =. then sec(8) =1 (Write your answer in the simplest form, use fractions whenever applicable

A: Explanation of the answer is as follows

Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 в) 9 c) 12 D)…

A: Volume

Q: Which of the following angle measure (in degrees) is coterminal to an angle of measure 660 degrees?…

A:

Q: ||r'(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). 3 r(t) = t'i + tºj %3| K(t) =

A: Use the given formula and find the required expression.

Q: Use a double integral to find the volume under the plane z = 22x + yand over the rectangle R = {(x,…

A:

Q: Two particles travel along the space curves r(t)and u(t). (If an answer does not exist, enter DNE.…

A:

Q: Finden- un) andrn - in twe dferent mays r(t) -n+ se's - e'N, wt) - t'k (a) re) - uch) () Find the…

A:

Q: Evaluate JJ xy dA, where R is the region in (1, 3) (5, 3) (2, 1) (4, 1)

A:

Q: Find the area of the region inside the circle r = 24 sin 0 and outside the cardioid r = 8 + 8 sin 0.…

A:

Q: Find the center of mass of the given system of point masses lying on the x-axis. - 6, - 3, m,- 6 X1…

A:

Q: For neN simplty 2-글 + 4-1 +8-금+16-습+. + +2"-그 2n

A:

Q: Using appropriate substitution xp: V9x2-36x + 37 Is equal to

A: We have to integrate given function

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Volume

Q: In sketching the graph of y=f(x) = 2sin -5, we translate the graph of y=2sin by 5 units downward and…

A: To translate the given function.

Q: r = V cos 20 r = 5 cos 0

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Solving

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

A:

Q: 1 -dt , find g'(2). V4 +t5 If g(x) =

A: Let's find.

Q: Find an equation of a line through the point (-1,3) making an angle of 45 degrees with the line…

A:

Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

A: