Write a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) = 25 – x2 dx 30 25 20 15 10 -6 4 6.

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Q: N/= (2+V1-x²)dx= %3D Hint: interpret the definite integral as an area. 4+ TI+8 2+ I 4 O 4 2+ T

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Q: (D) What is the value of the original integral in terms of x? -30V z2 + 25 X + C 25z

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Q: Use the table to estimate f(x)dx. 3 9 12 15 f(x) 51 49 45 37 25 15 | f(x)dx = i

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Q: (a) Evaluate the integral 40 dx. x2 + 4 Your answer should be in the form kr, where k is an integer.…

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Q: Find or evaluate the integral by completing the square. (Round your answer to three decimal places.)…

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Q: Find the area bounded by x² = 4y + 4 and x = y - 2. Using vertical element, what is the integral…

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Q: 2. Which of the following definite integrals represents the area of the shaded region? A. S²(4-x²)…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y,…

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Q: Using appropriate substitution, csC x cotx the integral S dx is equal to: e+csc x

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Q: y= f(x) -2- 2 4 8 Evaluate the following integrals by interpreting them in terms of areas: (a) f(x)…

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Q: What is the definite integral representing the area of the given region below? A. A= (1,1) В. А-D…

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Q: 1+x2 n = 10 Approximate the integral use the Simpson 1/3 Rule 4 dx n = 10

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Q: Which integral would represent the area shown below? The function is f(x) = = -2x + 5. 3- 21 1 X 1 2…

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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.