The graph above shows how the x-axis, the y-axis, the line y = -x + 3 and the curve %3D y = 2 sin x + 1create three bounded regions, labeled A, B, and C, in the first quadrant. Suppose region C is revolved about the x-axis. Which of the following integrals would describe the volume of the resulting solid? r2.850 Soso0 (-x+ 3)² – (2 sin x + 1)²dx r2.850 n J0,890 Sos90 (2 sin x + 1)² - (-†x+3)*dx O a fos00 (2 sin x + 1) – (-†x + 3)) *dx - 2.850 1)² - (-÷x + }'dx - 2.850 2

Q: Find the surface area if y = (x3/6)+(1/2x) on .5<=x<=1 is rotated about the x-axis.

A: Given: y=x36+12x on 5≤x≤1

Q: Find the areas enclosed by the following curves: x + y? = 3 4x + y? = 0 37 4x + y? = 0 %3D -1 -3-

A: Area between two curves

Q: Find the area of the region bounded by the graphs of y=x²-2x and y=x. Find the volume of the solid…

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Q: Q1.A: Find the area of the shaded region shown in figure (1). y = 1 y = x2 x 1+ y2 Figure (1) y = -1

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Q: Find the exact area of the region enclosed by a = t - 9t and y = 4t/2 and the y-axis. Be sure to…

A: To Find: The area of the region enclosed by x=t2-9t and y=4t1/2 and the y-axis.

Q: The volume V of a right circular cylinder of height 7 m and radius r m is V = V(r) = 7ar. Find the…

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Q: 1.Find the area enclosed by the curve y=x⁴ and y²=8x 2.find the area enclosed by the curve y=x²+1…

A: Thank you,Please rate my response.

Q: 8) The volume of the region in the second quadrant bounded above by y=-x3, below by the x-axis and…

A: The objective of this question is to find the volume of the region in the second quadrant bounded…

Q: Find the area bounded by the y2 = 8x and y = 2x.

A: To find the area bounded by the curves y2=8x and y=2x Solution :  Let y2=8x    ⋯(1) Since y=2x, we…

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.