Estimate the area between the x-axis and the graph of f(x) = 9 – 2° over the interval [0, 3] by using the three rectangles shown here: 101

Q: Find f, and f, for: z= 4x²-3xy+y.

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Q: dx Evaluate: 9 – x2 6,

A: folllow next step

Q: Use the function f(x)=x",x>0 to determine the bigger of the two numbers e' and a

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Q: 8 Use definition L{f(t)} = - S% e- 0 -st f(t) dt to find L{3t}

A: From definition of Laplace integral  for function ,, Here

Q: Use appropriate Lagrange interpolating polynomial to approximate f(8.2) , if f(8.3) = 17.56,f(8.1) =…

A: The value of the table for x and y: x 8.3 8.1 8.6 y 17.56 16.94 18.51 We will approximate…

Q: Consider an axisymmetric feeding bowl as shown on the left below. Its cross-section is shown on the…

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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.