Find the area of the shaded region. f(x) = x* - 8x + 21x, g(x) = 6x + 36 (3,54) (-1,30 by -10

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Q: Find the area of the shaded region. 1) f(x) = x3 + x2 - 6x %3D 30+ g(x) = 6x 20- (3, 18) 10+ (0:0)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: Find the shaded area enclosed by y = 8x² and y = x* – 8x² within –4<x<4. y- &r y-x* - 8r

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Q: i)Find the area of the region enclosed by graph of fx=x3-x2 and gx= 2x .

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Q: Find the area of the shaded region. f(x) = -x3 + x2 + 16x 30- 20- 4, 16) 10 g(x) = 4x %3D 6 X (3.-12

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Q: Find the area of the region between the graphs of y=17-x2 and y=-6x+10 over the interval -3<x<6.…

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Q: find the area of the shaded region.  f(x) = x^4-8x^3+18x^2, g(x)= -25x+102

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Q: Q2) A) Graph the curve Y = x (x +5)(x-3) between the value of x [-5, 3], then find the area of the…

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Q: Determine the area of the shaded region bounded by y = - x2 + 8x and y = x2 – 6x. The area of the…

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Q: Find the area of the shaded region.

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Q: Q-3: Find the area of shaded region in the shape: y = x2- 6x + 5 3 5

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Q: Find the area between f(x)=x²-12 and the x-axis from x = 0 and x = 2. The area is square units. ...

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Q: The area of the region enclosed by the graphs of y = x - 2x- 9 and y = x-9 is square units.

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Q: Find the area of the region below y= x^2- 4x+11 and above y=6 for 3≤X≤5

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Q: The area of the region between the x-axis and the graph of the f(x) = x3 - x² – 2x , –1 < x<2 is :…

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Q: Find the area of the region bounded by the graphs of y2 = 5 – x and y2 = 4x.

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Q: Q1: Find the area of the region between the x-axis and the graph of y = x' - 3x² +2x, where 0<x<2

A: Draw the graph and integrate with proper limits to get the area under the curve.

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Q: Find the area of the shaded region. f(x) = -x3 + x2 + 16x %3D 30+ 20+ (4, 16) 10+ -4 -2 4 6. х (-3,…

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Q: Find the area of the region enclosed by f(x) = a – 2x² and g(x) = a = 2².

A: Please see the answer in Step 2

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Q: Find the area of the shaded region. y y = 9x-x 20- 15- (7, 14) 1아 5- y= 2x 10

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Q: Find the area of the shaded region. 38) f(x) = x3 + 38) x2 - 6x 30- 20- (3, 18) 10 -4 -2 4 -10 -20+…

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Q: nd the area of the region under the graph of f(r) = 2r² – 4x + 2 on [-2, 3].

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Q: Find the area of the shaded region. f(x) =x - 8x° +21x2, g(x)= 20x+50

A: INTRODUCTION: If the straight line is above the curve in the bounded region, the straight line's…

Q: (b) Find the area of the region between the x-axis and the graph of f(x)=3x² – 3, where -2<xs2

A: The given graph is: fx=3x2-3, -2≤x≤2 The region is between this graph and x-axis.

Q: (b) Find the area of the region between the x-axis and the graph of f(x)=3x² - 3, where -2<x<2

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Q: (b) Find the area of the region between the x-axis and the graph of f(x) = -x - 2x, where -3s x<2

A: Explanation and solutions is given below....

Q: y2 =-x2 +2x+3

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Q: Let f(x) = 4 + 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 of the shaded region. f(x) = x* – 8x° +21x, g(x) = - 14x+ 136

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Q: Q1: Find the area of the region between the x-axis and the graph of y =x' - 3x +2x, where 0sx<2

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Q: Find the extreme values of f on the region described by the inequality. f(x, y) = 2x2 + 3y2 − 4x −…

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Q: Find the area of the region enclosed between f(x) = 0.9x²+ 6, g(x) = x, a =-8, and r = 4 Area =

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Q: Find the area of the region bounded by the graphs of the given equations. b) f(x)=2x2-6x+5,g(x)=x2+…

A: See below the answer and calculation

Q: Find the area between f(x)=x²-12 and the x-axis from x = 0 and x = 3. The area is square units.

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Q: y1=x2+2x+1 y2 =2x+5 Find the area of shaded region

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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.