Given the graph of the function f(x) below, use a left Riemann sum with 3 rectangles to approximate the integral r4.5 L° f(x) dx. Round to one decimal place.

Q: da (c) Use Romberg's method to compute correct to 4 decimal places by taking 1+2? h = 0.5, 0.25 and…

A: Trapezoidal Rule:                                      ∫abf(x)dx=h2[y0+yn+2(y1+y2+y3+...)] Given…

Q: Consider the following function: f(x) = 3x? – 2x +1 (1) Evaluate f(x)dr. Answer:

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Q: A conical tank (diameter= 4m, height=5 m) is initially full of water. At time zero, water discharges…

A: Given  Diameter of the tank = 4m Height of the tank = 5m

Q: The inventory for an item in a warehouse is given by I(t) = 90e0.03€ +, where t is measured in days…

A: We know for the year 2021, January, February, and March months have 31, 28, and 31 days. We have to…

Q: 2. Express each definite integral as a limit using summation notation: In x dx = L(8x – x²)dx =

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Q: A geiger counter is recording background radiation at an average rate of one hit per minute. Let T2…

A: The given solution is provided below:

Q: → (+,-) (- -) J (4)

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Q: Complete the following steps for the given​ function, interval, and value of n. a. Sketch the graph…

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Q: Evaluate the Integral. Take the integral from - pi/4 to pi/4 from the function 8 cost i + 7 sint j…

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Q: Calculate Rs for f(x) = 8- x over [3, 5].

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Q: Use the substitution x = 7 sint to evaluate the integral ſ √49 – x² dx.

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Q: The power P (in W) in an electric circuit is the product of the voltage V and the current I (in A).…

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Q: A 100-gal tank initially contains 25% dye solution. A 40% dye solution is allowed to enter at a rate…

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Q: Let f(t) = 201·(1.002)12·t.  Find f(7).  Round your answer to 2 decimal places.

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Q: Identify the appropriate substitution for the following integral: Sesin z cos adx

A: Assume u=sinx then du=cosxdx. Substitute sinx=u and cosxdx=du in the given integral.…

Q: At t, in seconds, your velocity, V, per second is given by v(t) = 6 + t², for 0 <t < 6. Using n = 2,…

A: Givenv(t)=6+t2, for 0≤t≤6Using n = 2 we need to evaluate left and right sum to estimate the meters…

Q: Find f "(x) if f(x) = e-*. f "(x) = %3D The solutions to f"(x) = 0 are x =

A: The given function is fx=e-x2. Formula and tip to be used The derivative of ex with respect to x is…

Q: use geometric rules to solve the following integral

A: The given integral: ∫13-2x+8dxWe have use geometric rules to evaluate the integral.

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.