Which integral corresponds to the area of the shaded region between the curves y = |a² – 4| and y = + 4? See the figure below for the indicated 2 region. 10- 5- -5 _0 2 (4 +4 (2? – 4) +4 2 + - 2 +4 (22 +4 ( 22

Q: 5. Evaluate the integral by interpreting it as an area 2 L(1 - 2) de |

A:

Q: Find V · (V × F) if F(x, y, z) = 3 sin xi + 9 cos(5x – 6y)j+ 10zk.

A:

Q: 4. Evaluate •5 (4 – 2.x) dx - 2,

A: topic - definite integral

Q: Find the area bounded by the indicated curves. y = x4 - 18x? + 81, y = 81 - x

A:

Q: dy Find for dx 2. y = x(e*) = x(e*)

A: Given: y=xex   ....(1)   As we know that; The Product rule; f·g'=f'·g+f·g' And ddxlnx=1xddxex=ex

Q: dP/dt= P(P − 10),

A: answer is in next step

Q: The region R lies on the lines x – y = 8, x + 7y = 8, x - y =| and x + 7y =

A:

Q: dx 2. x?V4-x2

A: Let x=2sin(u)⇒dxdu=2cos(u)⇒dx=2cos(u) du  and u=sin-1x2 ∫dxx24-x2=∫2cos(u) 2sin(u)24-2sin(u)2du…

Q: (x=1² +3t – 1 + 3t – ; at t=-2. t-2 y = t² +1

A:

Q: 81 fx, y) dy dx 10 10 O-10 10 1아 1아 -10 10 -10 -10 81 -x F(x, y) dy dx = f(x, y) dx dy

A: we have to change the limit of integration.

Q: 2. Find S +l" dudy by first snitching the order of integration 4

A:

Q: Summation of n = 0 to infinity of (x3n) / (n!) Find radius and interval of convergence.

A:

Q: Find the area of the region bounded by y = (1/8)(-x² + 6x + 7) and y = -6. Answer: Find the area of…

A:

Q: Express the derivative in "subscript" notation. NOTE: Your answer should take the form fo. dy dx?

A: Consider  ∂3y∂y∂x2=

Q: Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other…

A:

Q: t Attempt in Progress antity P is an exponential function of time t, such that P = 40 when t = 4 and…

A: for simplicity take P0=a Given  for t=4 , P=40 for t = 3 , P = 50

Q: 2. Evaluate f'(5) for y = v2x² – 1 hor Ju OIT

A:

Q: dx 2. x²V4-x?

A: Just use the trigonometrical substitution to make integral easy and then solved it.

Q: Problem 3 Find a power series representation for the function and determine its radius of…

A:

Q: 6. sin x (1 + sin x cos x) dx y csc² ( tan (y²)) dy 7. cos²(y²) sec (11w) tan (11w) V (2 – sec…

A:

Q: its magnitude and direction angle. 14. ļu| = 8, 0 = 225°

A: Topic:- vector algebra

Q: an best be evalu er Formula nometric Transf nometric Formu

A: We have to choose the correct option from the given options according to the given information

Q: Describe the graph of the equation. r = 3 cos t i – 18 sin tj+ k O An ellipse in the plane z = 1,…

A:

Q: L 32 da = 65 %3D Select one: O True O False A2Vadx = 104/3 Select one: O True O False S (+4)(a+3)da…

A:

Q: Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the…

A: Write an iterated triple integral in the order dz dy dx for the volume of the region in the first…

Q: Find the area bounded by the indicated curves. y = 3x + 3, y = x2 + 3 Optional For visualization,…

A:

Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

A:

Q: Evaluate the line integral |-ydx + xdy along the curve C : y² = 24x from (24, 24) to (0, 0).

A:

Q: Find the vector, given its ma 13. Jul 10,0 = 75° %3D %3D

A:

Q: 7. Find the area of the shaded region. Give the exact value for the answer. V = = sec?x y = cos x 4

A:

Q: x = -3x1 – 2x2 x2 = 9x1 + 3x2 %3D

A:

Q: 3. Find the values of x of the curve y = 3x where y' = y" 15

A:

Q: 5. Find the area of the region bounded by the xr-axis and the graph of f(x)= -over the interval (-o.…

A:

Q: Find dy for dx 6) In y = In xe*

A: Topic:- derivatives

Q: Find the area of the plane region bounded by y = x - 4x and y% x(2-x). Answer

A: As per Bartley guidelines we are supposed to answer only one question per post.  This post contains…

Q: x³dx is equivalent to Using trigonometric substitution, Vx² –4 A 6/ tan*0 seco do B) None © 8 sec0…

A: I am attaching image so that you understand each and every step.

Q: Solve the following initial valued problem x²y' + 2xy = e*, y(1) = 0

A: To find the solution of the given initial value problem.

Q: $3000 is invested in an account at interest rate r = 0.035, compounded continuously. (Round your…

A:

Q: For bER, b>0, b÷1, which of the following is not a property of the exponential function f(x) =b*? A.…

A: We  have to find out about exponential function

Q: Determine the integral of the ff. functions. 1. S - 10 sin 5x dx 2. S 4 x cos x² dx 3. S sec 2 (3x +…

A:

Q: a jə et v = (560, –335). Find the following: a. The magnitude of the vector. b. The direction of the…

A:

Q: Find the magnitude of vector AB. 1. A = (4, -3) and B 2. A = (-2, 11) and B = (2, 8) = (-8, 2) %3D…

A:

Q: Find an equation of the largest sphere contained in the cube determined by the planes a 1, a = 7, y…

A:

Q: Find the exact length of the curve. =글Vy (y-3), 16 <y< 25 X =

A:

Q: 7) Last problem!!! I want you to compute both sides of the equation in the Divergence Theorem The…

A:

Q: Evaluate the double integral using single applications of Simpson's 1/3 rule 2 (x2. 3y2 + xy³) dx dy…

A:

Q: dy Find for dx 3) y = In(vx2 + 1+x) sin¯1x X.

A:

Q: Ise the function f and the given real number a to find (f-)'(a). (Hint: See Example 5. If an answer…

A: We have to find out the derivative

Q: One of the correct steps to evaluate x2inx x²Inx dx to yield the correct integral A x?Inx B 1 x3 dx…

A:

Q: Jy csc?y dy is equal to A —у сoty — coty dy - Scon dy у сoty coty dy с) -у соѓу+ coty dy D) None E у…

A: