Sketch the region R and evaluate the iterated integral oral SSFS Salm x²y² dx dy f(x, y) dA.

The area D is the area in the XY-plane bounded by the X-axis, Y-axis, and the 4x + line5y = 0. Determine the maximum and minimum values f (x, y) = 2x2 + 2y2 - 4x - 2y + 3 in the region

Evaluate I SR 6xy5 dydx where the region is bounded by the curves y = x² - 1 and y=1-1². Sketch the two curves on the same graph and carefully indicate which curve is y=x²-1 and which curve is y = 1- x². 2

Find the area of the surface S defined by z = xy and x² + y² ≤ 3. (Use syntax like 2*pi/3 .)

Find the centroid of the region cut from the first quadrant by the circle x2 + y2 = a2.

Find the area of the region bounded by the parabola y = -x2 + 4x – 3 and its tangent lines at the points (0, –3) and (3,0). |