Estimate the area under the graph of f(x) = over the interval [– 3, 0] using four x + 4 approximating rectangles and right endpoints.

Q: f(x) = 4x² + 5x + 5; [-3, 3]

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Q: Estimate the area under the graph of f(x)=1/x+3 over the interval [-1,2] using ten approximating…

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Q: 4. Area Estimate vs Actual a) Estimate the Area beneath f(x)=-x' +18x² – 8x + 20 on [4,12] using 5…

A: Given that the function is fx=-x3+18x2-8x+20 on 4,12. It is required to find the estimated area and…

Q: Estimate the area under the graph of f(x)=x^2+2x from x=3 to x=11 using 44 approximating rectangles…

A: We have to estimate the area under the graph of f(x)= x2+2x from x=3 to x=11 using 44 approximating…

Q: Determine the area, in square units, bounded above by f(x)=−x^2−10x−16 and g(x)=2x+16 and bounded…

A: Given that fx=-x2-10x-16gx=2x + 16 The objective is to find the area of the region which is bounded…

Q: Find the area under the graph of f(x)=1+x^2 and from x=-1 to x=2 a) Use 3 rectangles and right…

A: All the parts have been done.

Q: Estimate the area under the graph of f(x) = x² from x=0 to x = 5 with five approximating rectangles…

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Q: What is the area between the graphs of f (x) = 3x + 5, g(x) = -2x – 3, x = 2, and x = 12?

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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.