0 Use integration by part to evaluale the falowing integrali x Inx-x dx 2 Evaluate +4x+3

Q: y=x3 2

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Q: 2x+ Vx* – 3Vx Find the integral | 5/ 2

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Q: VIn3 2x 3. Evaluate the double integral S Se*dydx 0 0

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Q: Use a substitution method to evaluate the integral

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Q: Evaluate the integrals

A: The given integral is ∫-151564-25x2dx. Evaluate as follows.

Q: +00 dx Evaluate the improper integral x(In x)²

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Q: J 3x + 2 6x² + 8x + 5 -dx

A: Let 6x2 + 8x + 5 = t Then, we differentiate it to form integral in t

Q: Compute the integral 4x + 8x³ dx. x4 + 16

A: The given integral is, ∫4x+8x3x4+16dx. Rewrite the given integral as follows.…

Q: 7. Find the complete integral of Pi P2 P3 + p4 x1 x2 x3 X4 = 0.

A: The given equation is, p1p2p3+p43 x1x2x3x43=0 This can be written as,…

Q: .3 2х+x-1 4. J dx х3+x2—4х-4

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Q: ¹ + ²*) *J x² dx (x² + 1)²(x² + 2x + 2) ·

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Q: / Evatuate integrals t 16 dx 2x VLAX 6 dx 4-25Y 2-

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Q: Evaluate the integral S dx 25+225x²

A: Given, ∫125+225x2dx

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.