Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves x = 0, y = 1, x = y° , about the line y = 1. Question Help: Video Check Answer

Q: dx /1 + 6x²

A: We have to find integration.

Q: Solve the initial value problem (b) y^ prime +2xy+xy^ 4 =0 ; y(0) = 1

A:

Q: Evaluate the definite integral. sin(3t)dt

A: I=∫0π3 sin(3t) dt  =-cos(3t)30π3  =-13 cos3π3-cos0

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A:

Q: 3. Suppose that the revenue in selling x tables is equal to 200x – 0.25x2 dollars, and producing a…

A:

Q: Find absolute maximum & absolute minimum f define on C0, 2]

A: maxima minima

Q: 1. [5.1] Determine the equation of a line tangent to the curve of x = 1. f(x) = 5e* +1 at 2. [5.1]…

A: A detailed solution is given below

Q: Use Stokes' Theorem to evaluate F. dr. z = 4 – 22 – y? F(x, y, z) = 2zi + 10xj+ 3yk where C is the…

A:

Q: Determine whether the vector field F(x, y, z) = (y + z)i – xz°j+ (x²siny)k is free of sources and…

A:

Q: Using any method, find the value of F. dr if F(1, у) — (бе" + ye")i + (e* + 5xe") j and at C :r(t) =…

A:

Q: encourage new members a bank offers a savings account of 2.4% interest mpounded monthly provided new…

A: We will determine the account value after 10 years.

Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti + t°j dt

A:

Q: 20.| sin³ }xcos" xdx

A:

Q: 28. The function f is given by f(x) = sin Which of the following statements are true? I. The graph…

A: Given,  f(x)=sin(x+1/x^2)

Q: Integrate the square root of sin (In x) dx * O x/2 [ sin (Inx) + cos (Inx)] + C x/2 [ sin (Inx) -…

A: Given

Q: Evaluate the integral. Show that the substitution x = V6 sec(0) transforms I into fcos(0) d0, and…

A:

Q: 2. Find the absolute minimum and the absolute maximum of the function f(x) = x* – 4r³ +5 on the…

A: Given, f(x)= x⁴-4x³+5 ; [1,4] Finding the first derivative we have  f'(x)=df/dx= d(x⁴-4x³+5)/dx…

Q: Given the Total Cost function, TC = 10 + 5Q?, find the marginal cost function, MC when Q = 10. [2]

A:

Q: A small business's cost to produce I units of a new product is given by C(x) = -0.001x+ 4x +506…

A: Solve the following

Q: Dy evaluating both integrals Ne ду dA y² dx + x² dy Əx for the given path. C: rectangle with…

A: We will verify Greens theorem.

Q: Use polar coordinates to evaluate the double integral of y(x^2+y^2)^2 dA, where R is the region…

A: Let's find.

Q: Power Reducing Formulas

A:

Q: Calculate ri(t) r2(t)] and [ri(t) × r2(t)] first by differentiating dt dt the product directly and…

A: Let's find.

Q: An inverted pyramid is being filled with water at a constant rate of 65 cubic centimeters per…

A:

Q: Question 1 A man on wharf 12 meters above the level of still water is pulling rope tied to a boat at…

A:

Q: 2. Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x²…

A:

Q: Q1/ Find the volume of the solid generated by revolving the region bounded by y = Vcos x, y 0 & Osxs…

A: Disk method: The disk method is used to find the volume of a solid when the axis of revolution is…

Q: Verify the formula F.n dS div FdV in the Divergence Theorem by evaluating the surface integral and…

A:

Q: | sin³(18x) dx =

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: This is a problem related to vector calculus. Based on the green's theorem we will answer the…

Q: Let g(t) give the total number of gallons of maple syrup sold by a local farmer over the first t…

A: The derivative is defined as an instantaneous rate of change at a given point. g(t) gives total…

Q: ||r(t) × r"(t)|| ||r"(t)||* Use the formula k(t) = to find k(t). r(t) = e"i+etj K(t)

A: We have to find k(t)=?

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A: Find your answer below

Q: Find the limits. If you use L'Hopitals Rule, make sure to justify why you can use it. 1- cos(2r) lim

A:

Q: Find the limit. lim (t i – 4 j + t k) lim (t i – 4 j+? k) i i+ i j+ i k

A: The given limit is; limt→9t i-4 j +t2 k

Q: Use Green's Theorem to evaluate the line integral. Iy? dx + xy C: boundary of the region lying…

A: A detailed solution is given below

Q: Evaluate the definite integral. Sols i + e*j+ t k at O e6 - 1 i+ 6 1 k i- i- (e 6 1 6 2

A: We know that integration of xn is xn+1/n+1. That is power rule of integration.     Here i attached…

Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

A:

Q: 10. Using the graph below of the function f(x), identify the approximate interval(s) where the first…

A: Given that,

Q: Determine whether F(x, y) = 3xi + 7yj is a conservative vector field. If so, find a potential…

A:

Q: 'ind the work done by the three-dimensional inverse-square field (r) = r on a particle that moves…

A: Given problem:-

Q: Evaluate the indicated partial derivatives. z = 6a?y – 4a°y dz dz ду

A:

Q: Find the derivative of the function at Po in the direction of u. X-y g(x,y) = Po(- 1,1), u= 12i + 5j…

A:

Q: Suppose that f is a function given as f(x) = - x² +x – 2. Simplify the expression f(r + h). f(x + h)…

A:

Q: 4. If u = (-3, 2), v = (-4, –6), find 4u – 7v %3D

A:

Q: Find the equation of the tangent line of y = 6e* at xo = 0. (Use symbolic notation and fractions…

A:

Q: find the flux of 3 – e")i+ (y³ + sin z)j+ (z³ – unded above by z = V4 – x² outward orientation.

A: We have to find the flux using the divergence therom according to the given information

Q: dx 4 XVx - 4

A: We need to find the solution for the given  integral by trigonometric substitution.

Q: Consider the solid obtained by rotating the region bounded by the given curves about the X-axis. y…

A:

Q: Use the formula k(t) %3D

A: