Consider the region, R, bounded above by f(x) = x² – 6x + 9 and g(x) over the interval 3,9. Find the area of R. = -3x + 27 and bounded below by the x-axis Give an exact fraction, if necessary, for your answer and do not include units.

Q: ii, Find the area under the graph y=5x⁴between the limits x= 1 and x=3.

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Q: Find the area of the region between the curves y=x²-1 and y=-6x²- +6 from x= -1 to x = 1. The area…

A: Area between two curves y=f(x) and y=g(x) from a to b is A=∫abfx-gxdx where fx≥gx ona,b We are given…

Q: Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to…

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Q: Let f(x) = 8 + 2x2. (a) Estimate the area under the graph of f, the x-axis, and the lines x = −1 and…

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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 the TOTAL geometric area bounded by the curve given by f(x) = x5 – x3 and the x-axis on the…

A: Given the curve is fx=x5-x3. Find the area bounded by the curve fx=x5-x3 and the x - axis y=0.

Q: b. Approximate the area bounded by f(x)=x² - 2x+6 on the x-interval [0,3] usingn = 3 rectangles 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: Find the area under the graph of y = 2x² - 2x + 4 on the interval [-2,0].

A: y=2x2−2x+4 on the interval [−2,0]

Q: Find the area bounded by the curves f(x)=x+8 and g(x)=x²-x.

A:

Q: area bounded by f(x) = 9x² – 2x + 1, the x-axis, x = -2 and x = 1

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Q: Find the area bounded by the graphs of f(x)=x+2, g(x)=3x²+5 , x=-1 and x=1.

A: Explanation of the answer is as follows

Q: Estimate the area under the graph of f(x) = 0.5x2 + 1 over [0, 6] and n = 6

A: Given: f(x) = 0.5x2 + 1 over [0, 6] and n = 6

Q: I have done part A, and attached it as an image, I need parts B and C please: B) Repeat part (a)…

A: We have to estimate the area by using left endpoints and mid points.

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.