2 4-y²² #13 Given S² S√4-y 0 0 (y) ddy (a) Write down inequalities. in xy representing the region R of integration, and sketch, Rin the xy-plane. an (b) Rewrite the given SS as equivalent integral using polar coordinates. (In the book they say "change Cartesian integral into a polar integral".) (c) Evaluate the integral from part (b) 12

Q: Choose the correct region of integration 10 (x² + y²) dy dx. Assume that in each figure, the…

A:

Q: 16-x² Choose the correct region of integration (x² + y²) dy dx. Assume that in each figure, the…

A: Given Integration

Q: (3) The following parts concern the integral below: ry dr dy. Vi-y² (a) Sketch the region of…

A: Answer

Q: Green’s Theorem for line integrals Use either form of Green’sTheorem to evaluate the following line…

A: By Green's Theorem, we have where R is the region enclosed by curve C.

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. S LvS- (x² + y²)…

A: Solve

Q: 9 vertices (0, 0), (,0) and (l, l). (a) Evaluate the integral 3. Let be Let C be the triangle with…

A:

Q: 1. (a) Without using a calculator, determine the following integrals: 8.x dr3; (1) 2+8r- 9 (1)/ (ii)…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 4: Use Green's Theorem to evaluate the following integral e dx + (5x+ 6) dy Where C is the triangle…

A: Using green theorem to evaluate the following integral.

Q: {(x, y) E R²; \x| + \y – a| < 1} andI= (y – 2x)2 y2 + 1 -dxdy. (i) Sketch the graph of the domain D…

A: We are given D=x, y∈ℝ2; x+y-x≤1  and  I=∬Dy-2x2y2+1 dxdy. For (i), Here, we need to sketch the graph…

Q: •1 L •√1-x² -1 J-√√1-x² 2-x²-y² x² + y² (x² + y²)5/²dzdydx

A: see my solution below

Q: 42. Converting to a polar integral Evaluate the integral dx dy. (1 + x² + y²)²

A:

Q: Consider 6 V 36-x² V 72-x²-y² r2 xydzdydx. (a) Describe the the solid region E of integration for…

A:

Q: Evaluate the integral fef ds, where f(x, y) = y cos(2x) and C is the triangle with vertices at the…

A:

Q: Use Green's Theorem to evaluate the line integral of F = (x², 6x) around the boundary of the…

A: