Consider the triple integral: (ʃ_2^3 ʃ_4^8 ʃ_0^10 sin(xy-z) dxdydz).  Use a change of variables to transform the integral to an integral over the cube:   {0

Q: Use integration by parts to evaluate the integral: fe-t sin( e-tsin(-10t)dt 1 - [ 101 sin(-10t) +…

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Q: What is the integral of 10pi(4-y)(sqrt(siny))dy from 0 to pi?

A: Let I=∫0π10π4-ysinydy Then, ∫0π10π4-ysiny…

Q: 2. Use the Fundamental Theorem of Calculus, Part 2, to evaluate the integrals: (a) π 3 secx (secx +…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Evaluate the triple integral (show all your work by hand!) |T| 2.xyz dzdydx.

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Q: Q2) Evaluate: So x sin 2x x² +9 .dx.

A: We use the Fourier transform to evaluate the following integral.∫−∞∞xsin⁡(2x)x2+9dx

Q: (a) /(3=² (За? — 6х + 5) dx - 1 .5 x° + 5 1 (b) dx - 4

A: To determine the value of definite integrals.

Q: Find the indefinite integral of r(t)=(-48t-20/3+5t+t^2)i+(arcsin(t))j+(cot(t))k

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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.