Interpret the definite integral A - f da = J L(*) dx as computing the area of a region in the xy-plane. Then one can think of the definite integral as:

Q: Compute the area between the two functions, where f(x) is the “lower” function.

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Q: Evaluate the definite integral (2 + x) dx by first sketching the region and then using a geometric…

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Q: Find the area bounded by the curve f(x) = -x² + 10 and the x-axis. Give your answer correct to two…

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Q: The area that lies between Z= 0.56 and Z= 0.89 is?

A: GivenThe area lies between z=0.56  and z=0.89

Q: Integrate the area between the curves f (x) = x and g(x) = x² from x = 0 to x = 7. Sketch the area.

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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.