R; Being the 1st region of the coordinate plane between the y = x line and the y=x² parabola, Determine if the integral given in the picture is convergent or divergent.

Q: Find the area bounded by the curve y = x exp(-x²), the x-axis and the vertical line passing through…

A: Given: The given curve is, The x-axis and the vertical line passing through the maximum coordinate.…

Q: Let T be the linear operator on R defined by T(x,,x, x) = (2x1, x, - x, 5x, + 4x, + x,). Then 7 is…

A: First express the linear operator in matrix form and then use the matrix to calculate the inverse…

Q: Q5/ Find the area of the region in the first quadrant that is bounded above by y = √x and below by…

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Q: 5. Rewrite using absolute value notation. 1 2 4 b) 4-3 3 4 4-3-2-1 1 2 3 0 1 2 3

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Q: Find the isogonal trajectories cutting at an angle of arctan 4 to the family of curves y = Inx + C.

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Q: y = 9 - x² and y = x + 3 is 125 6 square units

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Q: Q5/ Find the area of the region in the first quadrant that is bounded above by y = √x and below by…

A:

Q: Q4\A: Find area of zone bounded by curves y = x² y = 2x+8

A: The given curves are: y=x2, y=2x+8 Find the area of zone bounded.

Q: The area D is the area in the XY-plane bounded by the X-axis, Y-axis, and the 4x + line 5y = 0.…

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Q: calculate the area of the bounded figure from the graph of the function y = x²-1 and the axis Ox

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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.