Evaluate the following definite integral. arctan dx

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A: Topic = Integration

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A: We have to find the following definite integral according to the given information

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A: Given:                   ∫0π6tan xdx Rewrite using trigonometry identity:                 =∫0π6sin…

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A: The objective of the question is evaluate the definite integral.

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A: Integrate it.

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A: Given information: definite integral ∫341-x-32dx

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A: follow next step

Q: Find the indefinite integral. Remember to include a "+ C" if appropriate. Enclose arguments of…

A: I = ∫x1/12 -2Sin(x) dxI = ∫x1/12dx -∫2 Sin(x) dx

Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: Find the indefinite integral. Remember to include a "+ C" if appropriate. Enclose arguments of…

A: solution:-using the integral formula∫xndx=xn+1n+1∫sinx dx=-cosx

Q: Find the indefinite integral. Remember to include a "+ C" if appropriate. Enclose arguments of…

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Q: Find the value of the definite integral, if exists. (Not a calculator problem!) Exact answer, no…

A: Given : ∫01cosx3·x2dx

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Q: Evaluate the definite integral two ways: First by a u-substitution in the definite integral and then…

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Q: Find the indefinite integral using the substitution x = 8 sin 0. (Remember to use absolute values…

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Q: Calculate the definite integral. 8 dx dx = (Simplify your answer.)

A: The objective of the question is to calculate the definite integral.

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

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Q: Evaluate the definite integral below. [³dr dx Enter your answer in exact form or rounded to two…

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Q: Evaluate the definite integral below. 17 3 dx Enter your answer in exact form or rounded to two…

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A: Given query is to evaluate the integral.

Q: evaluate the definite integral from 0 to (1/3) of pi*tan(pi*x)dx

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A: Introduction: The antiderivative of a function is the indefinite integral, which is the opposing…

Q: Find the indefinite integral. Remember to include a "+ C" if appropriate. Enclose arguments of…

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Q: Definite Integrals?

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A: The given integral is,∫0πe5xsin(5x)dx

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A: We can take out 8 and then integrate

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Q: tan 28 高) dx sec 28

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A: Use integral rules

Q: Find the indefinite integral . ∫csc x cot x dx

A: Consider  I=∫csc x cot xdx let  csc x= t Thus csc x cot x dx =dt

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.