Use tlie kesidlue theorem and colaula re the integral (x-0 (x12)(x-i)(x+i)

Q: 3/2 1/2 q q 1 2 dq

A:

Q: What is the integral of f(x) = X within the interval [3, 6]? %3D 5. 4+ 3- 2- 1 O Area = 18 O Area =…

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

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Q: evulate the indefinite integral  x/((x+1)^2(x+2)^2) showcase all work

A: We have to find indefinte integral.Integral is given below:

Q: Using only the definition of RS-integral, evaluate .2

A: See below

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

A: We distribute the denominator.

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4x(1 – x² )dx = i

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Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 5 4x(1 – x² )dx = i

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Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. | 4x(1 – x² )dx = i -1

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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: Evaluate the integral using the given substitution. Show your analyses on scratch paper showing…

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Q: Evaluate the integral. In(x + 7) dx -6 NOTE: Enter the exact answer in expanded form.

A: The given integral,∫-66ln(x+7) dx

Q: Evaluate the integral using the methods covered in the text so far:                    ∫ 2xe4x dx

A: Consider the given integral. I=∫2xe4xdx Put u=2x in the equation. u=2xdu=2xln2dxduln2=2xdx

Q: Evaluate the integral. (Hint: Let x+25 = u?.) 5/x+ 25 -dp-

A: You can solve the given integral by using substitution as follows :

Q: 2. In r dr

A:

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

A: Given:

Q: Evaluate the integral using Algebraic Sub. x + a dx 3x a |

A: Just I have used the substitution to make integral easy and then solved it. Final solution is in the…

Q: (1) -dr x(x + 1)

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Q: Evaluate this indefinite integral: 12t^7-t^2-t+3dt

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Q: [(9)se x². d²+xdx + (x²-n²) y=0_ by substitution x== 1102 at 2 pt souhen Hence show that it has no…

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

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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: So (x²+3x+3) dx Theorem 4% f6) dx= lim f (xi) Ax where Ax= b-a and x= atcAX

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Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 3 | 4x(1 – x² )dx = -1 i…

A: Given that: ∫-134x(1-x2)dx

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. 7 (x2…

A: Given,           ∫17x2−4x+7dx

Q: de 1+tan 0 k/2

A: Let I=∫0π2dθ1+tan θ      I=∫0π2dθ1+sin θcos θI=∫0π2cos θ dθcos θ+sin θ     ....(1)Using property…

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

A: Solve definite integral

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

A: Let,

Q: Evaluate the improper integral | f(x) dx, where f : R → R is defined by x² + 3x, x > -5, f (x) = x <…

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Q: Evaluate the following integrals using the Fundamental Theorem of Calculus 3 16 x+x² - x4 dx

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Q: Evaluate the integral 0 2 0 2-x xdydx.

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Q: Evaluate the following integrals using theFundamental Theorem of Calculus. Explain why your result…

A: Given: The objective is to evaluate the integral ∫01x2-2x+3dx using fundamental theorem of calculus…

Q: Evaluate the indefinite integral by using the substitution u = 5-x' to reduce the integral to…

A: Given the integral

Q: Use a Table of Integrals to evaluate the integral. 2xdx J(x² + 2)ln(x² + 2)

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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: 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: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4 4x(1 – x²)dx = i -1

A: To find the value of given integral.

Q: (10x – 3x + 1)dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: S(2 + vx)³ Vxdx

A: See the details solution in below

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

A: Here given I=∫012dx1-x2 Since ∫dx1-x2=sin-1x+C

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 5 | 4x(1 – x² )dx = -1 i

A:

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: Evaluate the integral.

A: Here given integration can be written as…

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4 | 4x(1 – x*)dx = i -1

A:

Q: Evaluate the integral using substitution as an aid: x (2x* + 1)2dx

A: Consider the integral

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

A: We apply partial decomposition to calculate the integral.

Q: Evaluate the integral by making the given substitution.  x^5/ (x^6-7), u=x^6-7

A:

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 2 | 4x(1 – x² )dx = i -1

A: Given,    ∫-124x(1-x2)dx

Q: Evaluate the Integral Sec² √r √x dr Njw SYD

A: Given: ∫1832sec2xxdx To find evaluate the given integral.

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.