Use Green's Theorem to evaluate the line integral a-x)dx + (2x - x) d for the given path. C: boundary of the region lying between the graphs of y = x and y = x² - 8x

Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

A:

Q: 21. Let D denote the region between the parabola y = 8-² and the line y = x + 2. Compute ff 2x + y…

A:

Q: 3. Evaluate f 2xdx + (y + 2)dy along the rectangle with vertices (0, 0), (0,3), (3,3) and (0, 3).

A:

Q: c) Evaluate the line integral (x+2y)dx -2xdy along the following closed path, the circle x+ y= 25,…

A: In parametric form,

Q: Find the absolute extrema of the function f defined by f(x) triangular region R with vertices (0,…

A:

Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

A:

Q: No. of integral points lying inside the parabola y² = 8x and circle x? + y? = 16 are %3D (A) 15 (B)…

A: To find  The number of integral points lying inside the parabola y^2=8x and the circle x^2+y^2=16.

Q: Find and describe the region inscribed by the lines (x-axis), (y = -x+2) and (x = 2y-4) under the…

A:

Q: V4–x² – y² Let f(x,y) =- Shade the region in the x-y plane that corresponds to the domain of f(x,y)…

A: We are given the function f(x, y)=4-x2-y2lnx-y. For f(x, y) to be defined, we must have the domain…