Evaluate the integral [₁ F. dr. F(x, y) = (x² + y) i+(6x - cos y) j where Cis the boundary of the region R that is inside the square with vertices (0, 0), (8, 0), (8, 8), (0, 8) but is outside the rectangle with vertices (1, 1), (7, 1), (7, 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. [1 F. dr = i

Q: Sketch the region enclosed by the curves à - 5 = 4y and x − 21 = (y — 4)², and compute its area.

A: x-5=4y⇒x=4y+5     x-21=(y-4)2 ⇒x=(y-4)2+21 Area between the curves…

Q: Activity 2 Find the first derivative of the following: 1. y = ln (12x) 2. y = sin-¹ (x² + 3) 3. y…

A:

Q: Find the volume generated when the area in this problem (Find the volume of the solid generated when…

A:

Q: Evaluate [12x. (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

A:

Q: valuate the integral of the following using Miscellaneous Substitution

A: Given function f(x)=xx2+1we want to find the intengral of given functio

Q: A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a rate…

A:

Q: 2. Find the laplace transforms 3. Find the laplace transforms of f(t) = et³ of f(t) = ¹e²t (2t)

A: Note: There is no standard form of Laplace transforms of f(t)=et3. For (3),     L14e2t2t=14·…

Q: adius of the circular fan is 19 inches). Suppose the fan turns at a rate of 58 revolutions per mine…

A: We will find the speeds.

Q: 2 Let f(x) = ₂²5 on [-3, 1]. x+5 Find all numbers c in [-3, 1] for which the derivative is equal to…

A: We need to find values of c.

Q: Use the method of disks/rings to determine the volume of the solid obtained by rotating the region…

A: Solving

Q: Question The total monthly cost of a family plan depends on the number of phones, p, and the GB of…

A:

Q: The Bernoulli's form of the differential equation 2x³dy-− y(y² + 3x² ]dx = 0 is

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: 14. Which of the following has ex³-¹as an antiderivative? A. x²x¹-1 B. 3x²x³-1 C. 3xe*¹-1 D. xex -1

A:

Q: PS. Evaluate fff(3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0…

A: Solving

Q: A classmate claims that the following are true. Discuss how you would demonstrate that these claims…

A:

Q: dx S x² √√16-(x-3)² Let x 3 = 4sec 0 dx = 4 sec 0 tan 0 de Is the solution on the right track? If…

A: We have to find the integral.

Q: Calculate the derivative. g" (0), g(s) = es S+7 (Give an exact answer. Use symbolic notation and…

A:

Q: Calculate the first five derivatives of f(x) = sin(x). Then determine f(24) and f(25). (Use symbolic…

A:

Q: Write the equations in cylindrical coordinates. (a) 4x² + 4y² - z² = 9 (b) 7x - y + z = 3

A:

Q: (c) r(0 - 1) = -cos (0)i-3 sin(0)j (d) r(π/6+ At) - r(π/6) = (cos Ar-sin Ar-3) + (20 At- At 2 2 2…

A: We have to find the value of function.

Q: Using trigonometric substitution to evaluate:, find dx * √x + √2-x² dx, O 3 cosø dø O 3sec^2 Ø dø O…

A:

Q: 1. ff(x) dx + f(x) dx = 2. f f(x)dx - f₁² f(x) dx = 3. ff(x) dx + f₂f(x) dx =

A:

Q: Find the area of the region bounded by the given curves. Decide whether to integrate with respect to…

A:

Q: √25x2-4 -dx, 2/5 cosø dø 2/5 sec^2 ødø 2/5 seco tanø dø None of the choices

A:

Q: The Bernoulli's form of the differential equation x²dy+ (2xy-y³dx=0 is The Bernoulli's form of the…

A:

Q: Find all solutions of the equation in the interval [0, 21). COS +1=0 2x 3 Write your answer in…

A: This is a problem related to trigonometric identity. Based on the given interval and function…

Q: Solve the following differential equations of ẻ dx+2(xe - y)dy=0;

A:

Q: (a) Write the second-order linear differential equation to model the motion. (b) Convert the…

A:

Q: Verify Green's Theorem by evaluating both integrals for the given path. [x² αx + x² or = // (+1) ++)…

A:

Q: 3x a) fx5e³x dx 2x² + 3 c) f x(x − 1)² dx TU b) f sin³ xdx 4 d) f tan5x sec³x dx

A:

Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

A: The Maclaurin series for f(x) is given by f(x) = f(0) + f'(0)1!x + f''(0)2!x2 + f'''(0)3!x3 + …

Q: Describe the graph of the equation. r = − 17i + tj + (t²-1) k It is a parabola in the x = It is a…

A:

Q: The manufacturer of color televisions can sell 1600 sets to his dealers at $427 each. If the price…

A: The manufacture of color televisions can sell 1600 sets to his dealers at $427 each. If the price is…

Q: (1+x²)dx+(y− tan^'(x)) dx = 0;

A: (1+x^2)dy+(y-arctan(x))dx=0 (1+x^2)dy=(arctan(x)-y)dx dy/dx=arctan(x)/(1+x^2)-y/(1+x^2)…

Q: Let f(x) = √√√x – 2. a) Find f(x + h): b) Find f(x + h) - f(x): c) Find_f(x+h)-f(x). h d) Find…

A: We have to solve multiple part

Q: Let f(x) = 2x³7x+3 Use the limit definition of the derivative to calculate the derivative of f:…

A:

Q: = cot = C C In (x² + y²) + 4 arccot =

A:

Q: For f(x) = √x+1, find ƒ'(x) using the definition f'(x) = lim f(x+h)-f(x) h h→0 f'(x) = Using this,…

A: TOPIC -derivative using limits and equation of tangent line

Q: Find the area region bounded by the loop of y^2 = x(5-x)^2

A:

Q: @[² (d) √x-x (x² + y²)³/2 dy dx.

A:

Q: The price for a product is given by p=128,000 -0.2x², where x is the number of units sold, so the…

A: We will put Revenue=0 to find the value of x

Q: -The Bernoulli's form of the differential equation 2x'dy-y(y² +3x)dx=0 is

A:

Q: While measuring the side of a cube, the percentage error incurred was 3%. Using differentials,…

A:

Q: rocket is launched from the ground at an angle of 0.65 radians, and the rocket travels in a straight…

A: Given query is to find the height of the rocket.

Q: a = 6, c = 9, B = 128°

A: answer is in next step

Q: Given f(x,y,z) = x³yz². Find fy(1,1,1)

A:

Q: yo dx

A:

Q: 2. Write the given (total) area as an integral. (3 points each) a. The area above the x-axis and…

A: area

Q: 2- Determine lim[ v( x-1000)+10]/x x-0

A: We have to determine limit of given function

Q: ∫(√(cos(x)) (sin^3 (x)) dx) what is the answer to this integral?

A: