5) Sketch the graphs of the functions f and g. f(x) = x2, g(x) = 1/x2   Find the area of the region enclosed by these graphs and the vertical lines x = 1 and x = 3.     = ? square units

Q: (1) Sketch the graphs y = x¹(x+2) and y = x(x+2) for the domain [-2, 1] shading the areas between…

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Q: Approximate the area under the curve f(x) = 3²-1 on [2, 4] using midpoints and 4 rectangles (round…

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Q: Find area of the region under the curve - 2 y = and above the x-axis, for 9 < r<11. area =

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Q: Find the area enclosed by the graphs of a = f(y) = y³ - 26y + 10 and x = g(y) = 40 - 6y² - y³. (a)…

A: Given:The functions are  and To Find:(a) The intersection point(b) Functions that are to the right…

Q: 3) Use approximating rectangles to approximate the area under the curve y = 4 – x2 on the interval…

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Q: which is enclosed by the functions f(x) = 2x and g(x) = x³ – 2x. Find the area of this region,…

A: fx =2x , g(x) =x3-2x Here use formula of area of bounded region =∫ab|fx-gx |dx find  a and b here…

Q: 4. Area Estimate vs Actual a) Estimate the Area beneath f(x)=-x' +18x² – 8x + 20 on [4,12] using 5…

A: Given that the function is fx=-x3+18x2-8x+20 on 4,12. It is required to find the estimated area and…

Q: a) Estimate the area under the graph of  f(x) = 7 + 4x2 from x = −1 to x = 2  using three…

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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.