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

Q: Evaluate the integral.

A:

Q: Evaluate the integral. 3. (In(x))² x3 dx 1

A: I am attaching image so that you understand each and every step.

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

A:

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

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

Q: Evaluate the integrals using fundamental theorem. | (2 sint – 24) dt

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Q: 5. Determine if the integral is conve 0. exdx -1/2 V1-e 2x

A: Given query is to find integral converges or diverges.

Q: Evaluate the integral 169 S. 13 dx 3 x( In x)³

A: Given integral ∫13169dxx(lnx)3. The objective is to evaluate the integral.

Q: Estimate ë to five digits of accuracy by computing the integral of f(x) = 4/1 – x² for x € [0, 1].

A: Given fx=41-x2 and x∈0,1 I=4∫x=011-x2dx

Q: Use the limit definition of the integral to evaluate the integral 4 3 (4.2 - x²) dx =

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Q: Evaluate the integral. '3 8- In(x) dx x2

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Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. (x2…

A: Given:

Q: Approximate the integral of: f(x) = Vsin(x) + x* + 5 from x = -10 to x = -14 using N = 4 steps. (a)…

A: Given : f(x)=sin(x)+x4+5 a) using left hand sided rectangles We know that  ∫abf(x)dx=…

Q: dt (2 – t4)4 -1

A:

Q: Evaluate the integral / f(x) dx, where -1 -{ if – 1 < x < 0 if 0 < x < 1 -X - f(x) = 1-VT - x²

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

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

Q: Evaluate the integral. dx 4 - x3

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

A:

Q: S(1+- x3 dx 1+x2, 3

A: Topic- integration

Q: Compute this improper integral showing all steps.  integral of (x/(x^4)+9) dx from 0 to infinity.

A: please refer to the image below

Q: Evaluate the Integral / tanh (2x)đx. A @ --n|cosh(2x)| + C B -In|cosh(2x)| + C © 21n|cosh(2x)|+ C D…

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Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. (x2 +…

A:

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 following integrals using theFundamental Theorem of Calculus.

A: Consider the following integral: ∫-22x2-4dx=F2-F-2 Fx=∫x2-4dx=x2+12+1-4x+C=x33-4x+C

Q: Evaluate the integral. 3x In x' хр

A: Integration need to be done after proper simplification of the term.

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

A:

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. 6. (x2…

A: To Evaluate: The integral function using theorem 4.

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

A: Solve definite integral

Q: Evaluate the integral a* In(x) dr

A:

Q: Evaluate the integral by interpreting it in terms of areas. 4 |(1- x) dx -5

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Q: Find the indefinite integral. (Use C for the constant of integra 2 xp xV4 - (In x)2

A: Solution

Q: Calculate the Integral of the f (x) = x2 / (x ^ 3-2) function in the [1,3] interval according to…

A:

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. '4 (x2…

A: Using the definition of integral.

Q: Find the general indefinite integral. x* + 4x +1

A:

Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. 1 | 3…

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Q: In xdx

A: Formula:Integration by parts:∫ uv dx =u∫v dx -∫ dudx∫vdxdxI=∫ x5 ln x dxu=ln x, dudx=1xv=x5I=ln x ∫…

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: We have to evaluate the integral given below:-∫-2-1(x-3)dx -(i) using fundamental theorem of…

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: Definition used-        Integral is convergent if the limit exists and a finite number,…

Q: Evaluate the integral.

A:

Q: Evaluate the integral.

A: Given: The integral, ∫12x5lnx dx.

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

A:

Q: t3 et" dt

A: Given, ∫t3e-t4dt We have to evaluate the indefinite integral.

Q: Evaluate the integrals by subs;tu;on dp- V5+x c)

A: ∫-14x5+x dx

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. 6. (x2…

A: Given,            ∫16x2 - 4x + 7 dx

Q: Show that In xdx = x In x-x+C and use this result to determine the integral:

A:

Q: 5/(5x+5x^2+x^3)

A: We apply partial decomposition to calculate the integral.

Q: Find Lebesque integral of function on segment (0,1) f(x) = if- 7h+1

A: In the given question we have to find the Lebesque integral of the given function…

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.