Use a series to approximate the value of the integral with an error of magnitude less than 10-8. Round to 8 decimal places. The integral from 0 to 0.13 sinx/x dx

Q: 1100 L1100 * 79 4096 sin (x) dx =? O 100 l100 24097

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Q: 10 dx

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Q: dx Use trigonometric substitution to solve the integral

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Q: Estimate integal compasite. tropezoidal the Sint Using Yule. with h-0.25. Subject:. Numerical method

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Q: Evaluate [sin² (7x)dx using Simpson's method to four decimal places. take n = 6.

A: ∫01sin2πxdx       To find: Above integral using Simpson's method if n=6.

Q: What is the area under one crest of the sine curve, from x = O to x = n? y=sin x dx 1/2

A: Given problem:-

Q: 3 ſ dx – S sin²5xdx

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Q: Using Simpson's 1/3 Rule to approximate the integral .2 | sin(x)dx, n=10 What is CS,) ? Round off…

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Q: Determine how large the number a has to be so that 08. 1 dx

A: Solution is given below

Q: 105. A student made the following error on a test: re = xe-1 dx Identify the error and explain how…

A: ex is of the form ax For the function xn, n is an integer. ddxxn=nxn-1, n is an integer. Example:…

Q: Use Numerical Sums to estimate the area A = letermined by right endpoints. Use a calculator and…

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Q: Solve the integral. cos x dx J (1+ sin² x) arctan (sin x) 10.

A: To evaluate:                      ∫cos x(1+sin2 x)arctan(sin x)dx    ... (1)

Q: Evaluate the following integrals. sin" r 0. cos a kle

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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.