Use the fact that 1 +C 2e2 to either evaluate the improper integral -dr, or show that it diverges.

Q: -s(-+)( + }) 1. dt

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Q: Evaluate the integral, if it exists.  ∫Csc2 (3t) dt

A: ∫ cosec23tdtLet 3t=θ⇒ddt3t=dθdt3=dθdt⇒dt=dθ3-1

Q: Evaluate the integral. 7y 1-7y dy

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Q: ydy J-7-By-y

A: Given problem:- ∫ ydy/√(-7-8y-y2)

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

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Q: I.Evaluate the ff. iterated integrals.

A: Given that: ∫36dyy3y2-9

Q: Calculate the following integral by Simpson's method 3/8 with n= and verify the error obtained. In…

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Q: Evaluate the integrals using the trig substitution dx 1. x²Vx2 – 1

A: The given question is from the topic of Integrals

Q: Consider the integral -8e-2' dt If the integral is divergent, type an upper-case "D". Otherwise,…

A: Given: ∫-∞-1-8e-2tdt

Q: Use the Table of Integrals to evaluate the integral. x² V 4x² - 27

A: ∫341x24x2-27dx=∫341x22x2-332dxLet x=332sec μ .    limits                                  when x=3…

Q: 1= [3y/7-3y° dy

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Q: dt /4+t²

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Q: Use a substitution method to evaluate the integral

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Q: dt (2 – t4)4 -1

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Q: -- 11x + 2

A: ∫dx4x2-11x+2We need to find the integration of the above function.

Q: Evaluate the integral or state that it diverges. 14 -dp- x(x+ 1) 2

A: The given integral ∫2∞14xx+1dx use partial fractions 14x(x+1)=14x-14(x+1)

Q: Find the integral of f(x) = 1 √1-16x² between 0 and 1.

A: The given integral is 1/sqrt(1-16x2).

Q: St³ In t dt

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Q: 1. S V16 – 4x²dx

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Q: Evaluate the integral.

A: Let the given intergral be y -y = ∫01r34+r2dry = ∫01r24+r2 r drLet,x = r2Diffrentiating with respect…

Q: Use this result to either evaluate the improper integral +oo 5xe dr or show that it diverges.

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Q: 9. dt 2 -4

A: ∫9t2-4dt=9·∫1t2-4dtLet u=\arcsec12t=9·∫secudu=9lntanu+secuSubstitute back…

Q: The improper integral 5dx is V1-x?

A: Since you have asked multiple, we will answer the first one. ∫015dx1-x2dxLet x = sin θ ⇒ dx = cos θ…

Q: Evaluate the integral 13t – 5| dt.

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Q: Find the complete integral of (p2 + q2)y = qz.

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Q: Evaluate the improper integral or state that it is divergent. 2 dx 1 64 + x2 0.

A: The given improper integral is ∫0∞264+x2dx. Evaluate as follows.

Q: The improper integral 2dx is 1-x2 0.

A: π

Q: evaluate the integral using the methods covered in the text so far.

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Q: 1 dx 1+ Vx 3

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Q: t * et  Compute the convolution integral.

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

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Q: What is the integral of 1/x from x=3 to x=6?

A: Solve definite integral

Q: Evaluate the integral from 0 to infinity of 1/[x2+5x+4] or show that it diverges

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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: Evaluate the integral or state that it diverges.

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Q: Evaluate the integral. inegral  ax / (x2 - bx ) dx

A: Consider the given integration as I=∫axx2-bxdx⇒I=∫ax-bdx

Q: Evaluate the following integral. ∫ 2z5e1-z dz

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Q: or show that it is divergent Evaluate the integral dx 10

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Q: Evaluate the integrals ∫√(25 - t2) dt

A: We have to evaluate the integral: ∫25-t2 dt Rewriting the integral, ∫25-t2 dt=∫52-t2 dt We know the…

Q: V1+ vz dz

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Q: Use the indicated entry in the Table of Integrals to evaluate the integral. 2 9V 4x2 – 3 dx; entry…

A: Solve, as follows: I=∫1294x2-3dx=18∫12x2-322dx

Q: Evaluate the improper integral or state that it is divergent. dt 2- 4t

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Q: What is the integral of (3t – 1)^3 dt

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Approximate the integral V1+ x³dx using:

A:

Q: Solve the integral equaher by eliminating the Inkegral = -3+) (3t -3ty(t) dt. = -3 for when ansusemg…

A: Differentiating both sides of equations. Differentiating integral using leibniz's rule.

Q: Evaluate the improper integral or state that it is divergent. dt 2 - 3t 4-

A: Given that: ∫4∞dtt2-3t

Q: Use the fact that 2e2 4e2r to cither evaluate the improper integral / dr, or show that it diverges.

A: Let us define the given improper integral as shown below: ∫0∞xe2xdx=limn→∞∫0nxe2xdx

Q: Evaluate the improper integral dz, if it exist (x² + 49)2

A: Here we have to evaluate the given improper integral.

Q: Suppose we perform the substitution .3 u=9-x in the integral

A: Given that:∫123x29-x3dx

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.