Evaluate the definite integral. (x4 - Jo 5x + 6x) dx

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Q: x² – 2x dx

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Q: Find - 6x+1 x² +1 -dx.

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Q: Evaluate f(4 – 3x)³ dr

A: The integration of the (4-3x)3 and limit from 1 to 2.

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A: Evaluate the given integral as follows. Let u = x + 5 and du = dx and simplify as follows.

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A: The given integral is: I=∫x2-4x3dx

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Q: dx L2 exp %|

A: Given integral is I=∫-∞∞e-x2L2dx This type of integral cannot be done using elementary integration…

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A: Substitution method of Definite Integration : Suppose  and let  be continuous over an interval Let…

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Q: Evaluate -3)x+3 dx

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Q: Find. (x²+1)3 2x dx

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Q: 2 dx Evaluate J xvx4 + 25

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Q: x/x+ 3 dx

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Q: 2х -1 -dx. x +3 Evaluate

A: Let,           I=∫2x-1x+3dx

Q: Evaluate х2 + 2х — 1 х3 — х

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Q: Find ?Va² - x2 dx

A: Explanation of the answer is as follows

Q: dx x-6x

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Q: x2 dx 21. 7-5x3

A:

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.