d csinx 1 dt dx '3 1-t2 V5 t vt2 +1 dt Si Vx V1+ xVxdx

Q: 7x2 V2x3 - 1 dx .2.

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Q: Find the general integral and compute 3 diferent solutions for : xzx+(x+z)zy=y-x

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Q: 2. Suppose | 29(r)dr = 10. Using linearity properties of integrals, calculate | (g(x) + 3)dx. 3

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Q: Evaluate the integrals: V2 1- dx (T/2 7cost sin t dt 2-

A: as per our guidelines, I am solving only the first question with both parts please resubmit other…

Q: Evaluate the given integral with suitable substitution : 5z 10r (20 + 20) dr

A: Explanation of the solution is given below...

Q: VE dt 42+T

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Q: 3 Calculate the integral: dx x² V25 + x2

A: Here first put x=1/t and then the expression inside the square root as y^2. As showing in solution

Q: what is the integral of e^(-2a|t|) from -w to w?

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Q: The area between the curve X= t2 - 2t+1, y= In(t) and the y-axis for 1sts5 would be found by setting…

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Q: 2. Identify which of the following integrals are improper: 1 1 dx 1 fin(x)dx 1 X +3 1 fe* dr -dp- 3

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Q: Evaluate the derinite Integral. #5 In(x) dx

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Q: Evaluate the following integrals 5z (5 – z°)*dx A. 3 -dr 3 В. 6x + 5 c. /"zV9-z'dz С. 1 -dr 5 - edz…

A: Answer and explanation is given below...

Q: Evaluate the integrals

A: Given: ∫-3-1y5-2yy3dy for evaluating this limit we first separate terms then integrate it

Q: Q1) Evaluate the following integral using By Parts Method: х.In(x3 + x) dx

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Q: Use the method of u-substitution to evaluate the given integrals. 4t dt 2 – 812

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Q: 2. Compute the integral dy dx by interchanging the order of integration.

A: Order of change of integrals

Q: Calculate the following integrals: (6X-5)dx 3.1 I = S V3x²-5x+6

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Q: St³ In t dt

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Q: Evaluate the integrals ∫sech √t tanh √t dt/√t

A: Given, ∫sechttanhttdt We know that,  a.bc=a.bc =∫tanhtsechttdt Substitute the value of   u=t ⇒du=12t…

Q: dt (2 – t4)4

A: Given, ∫-10t3(2-t4)4dt

Q: ydy V16–9y* 4

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Q: 5. Evaluate the following improper integrals (if not shoW Wny). x² dx a- 00 4 1 dx -2 x+2 b-

A: To evaluate the improper integrals.

Q: h. fx2 Vx3 + 2dx

A: Integrate by substitution

Q: Evaluate only two of the following integrals: -16 In y a) S 8x² sin(4x) dx dy 4/y b) Jg 4Vý

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Q: 8r dr. 4. Evaluate the improper integral or show that it diverges:

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Q: 1. Evaluate the improper integral 150 xe dx or state that it diverges.

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Q: Which of the following evaluates the double integral xy dA,

A: We can solve this as follows:

Q: Evaluate the integral: Se³+ cosh2x33+ cosh2xsinh2x dx 3+ (3e)3 + cosh2x A + C 2+2ln3 (3e)3 + sinh2x…

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Q: 3 4-3x S²³ So dx dy

A: To evaluate the given double integral.∫03∫04-3x dx dy

Q: Evaluate the following IMPROPER INTEGRALS, It is optional to double check your answers/solution for…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Jy cosy smy dy 3

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Q: Evaluate the integral.

A: We have to evaluate the integral: ∫x3xx2+3y2dy Here we have to integrate with respect to y so x2…

Q: 3. Apply Romberg quadrature to •1 1 dx 1+ x2 for h = 1, 1/2, 1/4, 1/8. Show a table of approximate…

A: We are given the following definite integral : ∫1/(1+x2) dx from 0 to 1 And we have to solve it…

Q: of the following is an improper integral? • In3e COsx dx xe | in(x*+1) dx n(x++1)dr -4 x2-x- 2

A: Improper integrals are characterised as

Q: Evaluate the integrals ∫ e4t + 2e2t - et/e2t + 1 dt

A: Consider the following integral:…

Q: In y -dy 4

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Q: Evaluate the integral. Clearly indicate u-substitution steps if required. 19 J2+ 5y

A: Given integral is ∫195+2ydy evaluating the integral with u substitution

Q: Approximate the following integral with n = 4 using trapezoidal rule. 2 dx |x|Vx² – 1 1.5

A: The trapezoidal rule uses trapezoids to approximate the area. The formula below is used to evaluate…

Q: Evaluate the following indefinite integrals. 1. Jx²dx 2. S(x³ + 2x)dx 3. S(a)dt :a = constant

A: Solving the problem by finding the indefinite integral.

Q: Evaluate the Cauchy principal value of the given improper integral. 1 [ (x² + 4)² dx

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Q: Compute the following Gaussian integrals. 1. xte-aa2 dx 8. 2. xe-ax dr

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Q: Evaluate the integrals: (d) ∫(lnx)2dx. (e) ∫tan−1(3x)dx. (f)∫cos4(3x)dx.

A: We can evaluate the first two integrals by using  the integration by parts method. To evaluate…

Q: The area of a circle of radius v7 can be calculated using which of the following integrals? O 7- x²…

A: Before finding the area we need to see the formula for area under the curve f(x) for a≤x≤b is given…

Q: Express the integral L Ey.2) dadrdy as an iterated integral in the other five different ways.

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Q: Which of the following integrals are improper? (Select 3 L₁x²-1 dx 3x - 1 1 06²/21 x ² = 1 dx 2x 00…

A: Topic:-  improper integration

Q: Evaluate the integral. X √ ² ₁x + (x + 16y) dy

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Q: 7) Evaluate the integral Ver+9 dy

A: #7 as per demand Solve integration with help u substitution

Q: Find the integral of f (z2 +x2 + y33) dt.

A: Given : ∫z2+x2+y33dt

Q: Evaluate the following integrals using power formula. 1) S 3t dt 2) dy

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.