Use a graphing utility to graph the region bounded by the graphs of the equations. Use the integration capabilities of the graphing utility to approximate the centroid of the region y =8/(x2 + 4), y = 0, x = −2, x = 2

Q: find the area of the region bounded by the curves y=x3 and y = x² between their intersections.

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Q: Find the centroid of the region in the plane enclosed by the curves y = +-(1 - x2)^(-1/2) and the…

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Q: Use integration to find the area of the figure having the given vertices. (0, 0), (1, 6), (3,-2),…

A: We will find the area of the figure having the given vertices.

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.