6. Let f(x) = 6x – x². Sketch the graph of f(x) in the interval [0, 7] and describe in words what the definite integral r)dx represents in terms of areas. SET UP integral(s) for the total area between the graph of f(x) and the x-axis from x = 0 to x = 7. Your answer should not include any absolute values. You do not need to evaluate. If f(t) is the velocity of a particle moving along a line measured in meters per second. Find the displacement traveled (in meters) of the particle during the time interval 0sIs7.

Q: (Click on the graph for a larger version.) A. f3 f(x) dx = B. If the vertical red shaded area in the…

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Q: Approximate the area under the graph of F(x) = 0.2x³ + 2x² -0.2x-2 over the interval [-9, -4] using…

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Q: Estimate the area between the x-axis and the graph of f(x) = 9 - x² over the interval [-2, 1] by…

A: Given:   fx=9-x2 over the interval -2, 1. A graph is given with three rectangles in it. To find: We…

Q: Find and evaluate exactly an integral expression that represents the area between y = f(x) and the…

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Q: Help sketch the graph of the two functions and find the area between them using image attached

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Q: Find the area of the region enclosed by y = 5 – x² and 9 = x2 – 3 as a definite integral (do NOT…

A: To Determine :-  The area of the region enclosed by y = 5 - x2 and y = x2 - 3 as a definite…

Q: 4. Let f(x) = x² – 9 and g(x) = 2x – 1. (a) Draw both functions on the same set of axes. (b) On your…

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Q: Find the area between the y-axis and the graph X = 127 124 y² 2 1 -3 -2 -1 2 о T 4 3 0 -1 -2 1 on…

A: Given y-axis and x=1y2 on the interval -1,-3

Q: Let f(x) = 3 - x² and g(x) = 2x². Write an expression involving definite integrals whose value is…

A: we are given two equations and we need to form the equation that represent the area bounded by these…

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.