The analytical integration mostly achieves the true value of an integration of a function. However, there are numeral methods that can be used to find the integration value of a function such as Simpson's 1/3 rule and trapezoidal rule. In the below integral the angle is in radians. (12 + 3sinx)dx (a) Evaluate the integral using, (i) Single application of Simpson's 1/3 rule (Use 6 decimal places in all calculations) (ii) Multiple-application trapezoidal rule, with n = 4 (Use 6 decimal places in all calculations) (b) For each of the numerical estimates in part (a), determine the percent relative true error based on the true value (true value =14.066370)

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Q: I sin³x 5 sin x 4 cos x dx

A: To find out the integration.

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Q: f 4 sin 8x cos 3x dx

A: To find out the integration of the given integrand.

Q: Make Detailed solution INTEGRATION OF TRIGONOMETRIC FUNCTIONS

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A: The electrical supply, v, for an air conditioning unit is represented by the function: dvdθ=8 sin 3θ

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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.