Let the region R be the area enclosed by the function f (x) = ln (x)+1 and g(x) = x – 1. If the region R is the base of a solid such that each cross section perpendicular to the x-axis is a semi-circle with diameters extending through the region R, find the volume of the solid. You may use a calculator and round to the nearest thousandth. 6. 4 3 2 3

Q: Find the area bounded by the following curves. y=x", x= -1, x = 2, y= 0 The area is (Simplify your…

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Q: Let the region R be the area enclosed by the function f (x) = e®, the horizontal line y = 4, and the…

A: Given that , fx=ex And  y=4. If the region R is the base of a solid such that each cross section…

Q: The total area bounded by the graph of y = r- 1 and the x-axis is represented by 2.

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Q: A trapezoid JKLM is dilated through the origin by a scale factor of x. How does the area of the…

A: Suppose a trapezoid JKLM with coordinates, Jx1,y1, Kx2,y1, Lx4,y2, Mx3,y2 be dilated by a scale…

Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: Let the region R be the area enclosed by the function f (x) = x³, the horizontal line y = -1 and the…

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Q: Find the area of the shaded region. X y y=2e* x=2 =2x-1 X

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Q: Let the region R be the area enclosed by the function f(x) = x³ + 1 and g(x) = x + 1.Find the volume…

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Q: If x has a value of -4, determine if the series converges (absolutely or conditionally) or…

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Q: Let the region R be the area enclosed by the function f(x) = 2x³ , the horizontal line y = –3 and…

A: Given the region R be the area bounded by fx=2x13,y=-3,x=0,x=3. Visualize the solid: Each…

Q: Find the area of the given region. Use a graphing utility to verify your 1 + In x3 y = y 1 X. 1 3 4…

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Q: Let the region R be the area enclosed by the function f (x) = x³ – 1, the horizontal = 0 and x = 2.…

A: Given: The function: f(x) = x3 - 1 The horizontal line y = -4 The vertical lines are x = 0 and x = 2

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.