2) Sketch the graphs of the functions f and g. f(x) = x2 + 2,    g(x) = 1/3 x3   Find the area of the region enclosed by these graphs and the vertical lines x = −3 and x = 2.

Q: Find the exact area between f(x) = 2x and g(x) = 15 – x from the vertical axis to their point of…

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Q: Q4. Ca) Graph s=2sin3 (b) Evaluate the area inside the curve.

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Q: Find the area between the curves: y = x³ − 14x² + 40x and y = −x³ + 14x² − 40x 1280 3

A: Note:- Since the student has posted multiple questions and does not mention any specific question,…

Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² - c² and y = c² - x² is…

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Q: 4) Find the signed area and the absolute area of the region between the graph of f(x) = x² - 1 and…

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Q: Find the area of the shaded region (indicated below) between y = -x (dashed line) and y = √2-x…

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Q: (8) Suppose m > 0. Find the coordinates of the points (in terms of m) where y = mx in- tersects y =…

A: Here we have to find the area.

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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Q: c) Consider the following two functions are given: y = 2x - x² and y = x². i. Sketch the two curves…

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Q: 16. Find (1) the net area and (ii) the area of the region above the x-axis bounded by y=121-x².…

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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.