Evaluate the integral using lIntegration by Partsisubstitution, or both if necessary. In(In 10x) dx = +C 10x

Q: Evaluate the integral. dy yt – 16

A: Given:

Q: Evaluate the integral using appropriate substitution. an V3- a de + C

A: It is required to evaluate integral by substitution.

Q: Evaluate the integral. 16 In(y) dy Vy

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Q: O Calculate the integral y dydx

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: xp xy6x -x

A: The given integral ∫1x6x-x2dxThe integral formula,117. ∫duu2au-u2=-2au-u2au+C

Q: Express the iterated integral in the opposite order. dy dx

A: First option is the correct option. Find the region of the integration graphically. The value for y…

Q: Evaluate the integral. 6. Vy In(y) dy

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Q: Evaluate the integral by using a substitution prior to integration by parts |(In 9x)? dx Sams .....…

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Q: Evaluate the integral or show that it is divergent.

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Q: 4 dx, u= 1 + 2x (1 + 2x)

A: Explanation: Given that: ∫41+2x3dx,      u=1+2x Concept: 1. ∫xndx=1n+1xn+1+C Calculation: First…

Q: Make a substitution to express the integrand as arational function and then evaluate the integral.…

A: Given integral is: Using substitution and applying derivative:

Q: Evaluate the integral by interpreting it in terms of areas. | V1 – x² dx

A: Required answer is given in next step.

Q: Evaluate the integral dx (2x + 11) by making the appropriate substitution: u =

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Q: compute the value of the following improper integral. If it is divergent type D. dr (5x+1)

A: To compute the value of improper integral: I=∫1∞1(5x+1)2dx...(1)

Q: Evaluate the integral by making the given substitution.

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Q: In ly-y-cf dy

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Q: dw V5 – e-2

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Q: Evaluate the iterated integral by converting to lar coordinates. /1-(х-1)2 x² + y² dy dx

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Q: Express the integral in terms of the variable u, but do not evaluate it. relo In x dx; u = In x es…

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Q: Express the integral in terms of the variable u, but do not evaluat e21 In x dx; u = In x re21 In x…

A: We are asked to evaluate the integral.

Q: Compute the value of the following improper integral. If it is divergent, type "Diverges" or "D".…

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Q: Evaluate the integral: / In(r")) d.x.

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Q: Evaluate the integral using the given substitution. dx ,u = 6x + 1

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Q: dx (x + 2)3

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Q: Evaluate In x dx exactly by changing it to a dy integral.

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Q: Use Romberg integration to compute R3.3 for the following integral x sin x dx

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Q: Evaluate the integrals: A: So So x sin y dy dx

A: ∫0π∫0xx siny dy dx

Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

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Q: evaluate the integral using the Integration by Parts formula with the given choice of u and dv.

A: Given:

Q: b) [12x – 1|dx 2.x

A: The given integral ∫012x-1dx

Q: 1.5 x² In x dx

A:

Q: 14) ſe Vtanh® e" dy

A: Given that evaluate the integral

Q: The value of integral .dz is (z – 1)?

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Q: [2+v9-x)dx

A: Hello. Since your question has multiple parts, we will solve the first question for you. If you want…

Q: t * et  Compute the convolution integral.

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Q: Evaluate the improper integrals: (a): xe ,-x dx •4 dx (b) V4-x

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Q: Evaluate the integral 8x cos y dy dr y – 4 by reversing the order of integration.

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Q: Reverse the order of integratlon and then evaluate the Integral 10Tin6 Jinu! dx dy 9/10 et2

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Q: Find the integral using the substitution u = t3.

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Q: Evaluate the integral using integration by parts with theindicated choices of u and dv .   ∫θ Cos θ…

A: We have to solve the integral using integration by parts: ∫θ cos θ dθ taking u=θ, v=cos θ When two…

Q: Evaluate the integral. | (In(3.x))² dx = +C

A: From the given problem: I=∫ln3x2dx  ....(1) Let, t=3x So, ddxt=ddx3xdtdx=3dx=13dt Nw substitute…

Q: Evaluate the integrals

A: Evaluate∫−π3−π44sec2t+πt2dt

Q: Consider the integral 7x – 21 da 2x – 3 If the integral is divergent, type an upper-case "D".…

A: the given integral is ∫027x-212x-3dx

Q: x In(2 + x³) dx

A:

Q: Sy²sin (2y) dy

A: Integration by parts.

Q: z · 3°dz

A:

Q: (e2x –1)2 dx 1. e 2x

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Q: Compute the integral | x"dx, with a=1, b=7, and N=5. Answer to three decimals.

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Q: Evaluate the integral using FTC I.

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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.