Set up the integral that gives the area of the shaded region and total area under the shaded reagion.

Q: Sketch, shade, and label the region bounded by the functions у %3 х2 + 2 апd у %3D 2x + 5

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Q: Find the area under the curve, interval is 10m and ordinates are  0,7,11,15,0.

A: To find - Find the area under the curve, interval is 10m and ordinates are 0, 7, 11, 15, 0.

Q: rea of the region enclosed by

A: we have to find the area of the region bounded by the curve, y=2-x2 .....(1) and the line y=-x

Q: Determine the area of the region enclosed by the Y-2x = -1 and 4 = x ² = 4x+4. Do not simplity…

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Q: Find the area bounded by the curve x²=y+2 and the line x+y=0

A: Integrals and derivatives are considered as the inverses of each other. For example If we integrate…

Q: y=x² 3y=2x+ (1, 6) 6. 4. (2, 4) (-2, 4) 2 y= 8 - 2 x

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Q: Sketch the region between y=x^2 +x-2 and the x axis over the interval [-5,2]. Find the area of the…

A: Consider the given equation of the parabola, y=x2+x-2 To draw the graph of the bola first we need to…

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.