The following table gives the approximate height (in meters) at quarter-meter intervals of a mound of gravel. 0.75 0.2 0.5 0.5 0.25 0.2 0.5 0.5 0.6 0.8 0.7 0.5 0.25 0.25 0.5 0.7 0.6 0.5 0.2 0.25 0.5 0.25 0.2 y / x 0.25 0.5 0.75 1 Estimate the volume V of the mound by computing the average of the two Riemann sums S4,3 with lower-left and upper-right vertices of the subrectangles as sample points. V = 3 m

Q: Find the distance between the origin and the normal to the curve y=e2x+x2 at the point where x=0…

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A: Given:   To determine: ∠OXY

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A: See attached file for a step by step explanation.

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A: We can find the answer as given below

Q: Y 59° Z. 138°

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A: find the length of both polar curve as following:-

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A: Given: Now,

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Q: S arctan y dy y3

A: Let's evaluate given integral.

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A: Answer is mentioned below

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Q: (c) Determine the natural cubic spline that interpolates the data f(0) = 1, f(3) = 2, f(8) = 3 and…

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Q: a) In exercise 1.1, describe the erro statement of the tangent ratio.

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Q: Find the arc length of the graph of the function over the indicated interval. 3/2 y -1 y 40 30 20 10…

A: The arc length of of a function f(x) from a to b is given byArc length=∫ab1+f'x2 dx .Here,…

Q: 10) Find the Area of the sector of the cirde Rand your an swer te nearest tenths 1 Substitute into…

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Q: (c) Determine the natural cubic spline that interpolates the data f(0) = 0, f(1) = 1, f(3) = 4 and…

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Q: nd the length of a tangent drawn to a circle of radius 3.2cm from a point which is 5 cm away from…

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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.