(a) Find an approximation to the integral  ∫04      (x2 -3x) dxusing a Riemann sum with right endpoints and n =8.(b) Draw a diagram like Figure 2 to illustrate the approximationin part (a).

Q: b) Determine the numerical integral of the function h(x) =√1 + x^4 from x = 0 to x = 2 using…

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Q: Show that the right Riemann sum R6 approximation of (1 + 3.r)dr is 51

A: Given ∫-15(1+3x)dx  Using the right Riemen sum R6 approximation of the given integral we get  5--16[…

Q: Write the following expression in algebraic form: sin(arccos (6x)) V1-36z2 O VI – 36x² O VI – 6x² O…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Use integration by parts to prove the reductionformula.

A: Consider the following integration by parts formula: ∫uvdx=u∫vdx-∫dudx∫vdxdx ILATE Rule: We have two…

Q: Evaluate the triple integral 2-z²-y² 1₁. [27/²² (x² + y2)3/2 dz dy dx. z²+y²

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Q: а) 5 4х x² + 4 sin (x)| .2 3

A: Given integral is ∫354xx2+4sinxdx Take Note:- As per our guidelines, we'll answer the first one as…

Q: 53) Rewrite the integral (-1/1)(x²/1)(0[1-y) f(x,y,z) dzdydx

A: Rewrite the triple integrals

Q: Evaluate the integral(mx+b)/(x-p)(x-q) In the integral m,b,p,q are constants and p is not equal to…

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Q: 8) Estimate ₂x¹dx using the average of a left-hand and right-hand Riemann sum with n = 5. You can…

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Q: AB5: Use a left Riemann sum with the three subintervals indicated by the table above to approximate…

A: Riemann sum is a method to approximate a definite integral. There are two different kinds of…

Q: We will try to compute the real integrale-1²/²e-itz dr. Let R> 0 and let y be the rectangle with…

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Q: Which integral can be approximated by a right Riemann sum where f(x) = 2x3 + 3 on the interval [2,…

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Q: 2. Use the Riemann sums to calculate the exact area under the curve and above the axis a) f(x) = 2x³…

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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.