Exal Express the integral I| 2x²ydA 3x²and as an iterated integral, where R is the region bounded by the parabolas y y = 16 – x2 . Then evaluate the integral.

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

A: 80π

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

A:

Q: Find the area under the curve 2x+3y-6%3D0 from x+63D0 to x-19%3D0

A:

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

A: (.)  Given ,  Area of the surface S defined by z=xy and x2+y2≤3 .   If  z=f(x,y) ∀ (x,y)∈R  the…

Q: enclosed betw parabola y = x2

A:

Q: The area D is the area in the XY-plane bounded by the X-axis, Y-axis, and the 4x + line 5y = 0.…

A:

Q: Determine the integral: x²cosxdx (Α x²sinx-2xcosx-2sinx + C x²sinx + 2xcosx+2sinx + C x²sinx-2xcosx…

A:

Q: Use a change of variables to find the area of the curved rectangle above the x-axis bounded by…

A: Given,Area bounded by:y24-1≤x≤4-y216 , y264-16≤x≤9-y236 , x≥0

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.