Directions: Using the substitution rule. evaluate the following definite integrals. Answer it on a separate sheet of paper. 5. (e² + 1)² dr 6. dt

Q: Evaluate the following integrals. You must show all steps to earn credit. (a) dx. Hint: As a first…

A: A detailed solution is given below.

Q: Find the definite integral. You need not simplify your answer. | (x° + e° – e*) dæ 1. •4 t dt Jo v[?…

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Q: 1. Find the general indefinite integral or evaluate the definite integral, as necessary. a) S(3x² +…

A: We have to solve

Q: (b) [(x+1)e¯ 4r² 8r+l dr

A: Given, ∫(x+1)e-4x2-8x+1dx

Q: h(x) d f(t) dt dx (x)6 You must justify this formula with properties of definite integrals and…

A: Given : ddx∫gxhxftdt

Q: Find f 6x dx? А. х2 + с В. 2х2 + с c. +c D. Зx2 + C

A: This is a problem of indefinite integral. Based on the general formula we will answer the question.

Q: | (-3t3 + 6t – 6t +1) dt Evaluate the definite integral given above. Enter your answer as an exact…

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Q: Q4/ Answer the following: (a) Simplify the function y = |x- 1|+ |x+ 1. Moreover, compute the…

A: Consider function: y=x-1+x+1. Calculate- ∫-22x-1+x+1 dx. Since, x-1=    x-1 ,   x≥1-x-1,   x<1…

Q: Evaluate the following indefinite integrals. You do not need to simplify your answers. i. SG. +…

A: To evaluate: ∫2x+6sin3x-e5+12x3dx. Formula's used: ∫1xdx=lnx+C∫sinaxdx=-1acosax+C∫xndx=xn+1n+1+C…

Q: Evaluate the following definite integrals. Note: Final answer should be expressed as a decimal, not…

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Q: Assume function given(44) . Evaluate the following integrals(45), if possible.

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Q: a) Evaluate the following Integration by parts for definite integrals. i) So xe-s*dx ii) 12 Sin-'dx

A: The given integration is  I) ∫01xe-5xdx II) ∫032sin-1xdx

Q: dx When evaluating the definite integral / Te why must you 16 – x2" choose the antiderivative–coth…

A: Given:              ∫68dx16-x2 why must you choose the antiderivative 14coth-1x4 rather than…

Q: 2. Evaluate the following definite integrals. Note: Final answer should be expressed as a decimal,…

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Q: Evaluate the following definite integrals. Note: Final answer should be expressed as a decimal, not…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Evaluate the following 5 integrals. You do not have to simplify your answer. 12 1.) /3 1 + 1+x? 5e"…

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Q: Determine whether the following functions below is a solution or not a solution of the integral f(1-…

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Q: 3 (х3 — Зх2 + 4х — 5) dx | a) Approximate the definite integral with the Trapezoid Rule and n = 4.…

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Q: sec?xdx Which of the following is the same as which will lead us to the correct evaluation of this…

A: We will find a integral which is similar to the above and can be solved.

Q: Evaluate the definite integral (За3 — 5а + 2) da fo 5а + 2) dx — a) Find an anti-derivative +C b)…

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Q: jocos" (r² –6+ +1) di 2 4

A: Find the derivative

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 14tj – 6VEk) dt 3 A+…

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Q: c) Evaluate the following Integration by parts for definite integrals. i) 11) , 2 Sin-1dx

A: To evaluate the definite integrals by using integral by parts rule.

Q: V13 Use change of variables (substitution) to evaluate the definite integral S,° x(x² + 3)z dx

A: The given definite integral is, ∫113xx2+332dx

Q: Q4/ Answer the following: (a) Simplify the function y = |x – 1| + |x + 1|. Moreover, compute the…

A: The modulus function f(x)=|x| is defined as f(x)=-x for x<0, f(x)=x for x>0, and 0 for x=0.…

Q: Q4/ Answer the following: (a) Simplify the function y = |x – 1| + |x + 1|. Moreover, compute the…

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

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dt cos?(t) V7 + tan(t)…

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Q: | x(6+ x?)10 dx, u = 6+ x? æ(6 + a?)0 dx, 2

A: To find: The integral of ∫x6+x210dx. Given: The integral is ∫x6+x210dx. Formula used: The power rule…

Q: Directions: For 10 & 11, Evaluate each definite integral by using the antiderivative or geometric…

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Q: z(32² – 1)° dz etermine the value of the definite integral given above. Enter your answer as an…

A: To find:∫01x3x2-15dx

Q: ch of the following integrals is equal to the integral / f(3x-5) dx? ) dr? 7/3 ) dz

A: Please refer to the image below

Q: Which of the following properties of definite integral is INCORRECT? -2 3 f(x) d=F(2) – F(1)} 3 2 2…

A: We have to find which of the following properties of the definite integral is incorrect.

Q: Extra Credit Find the following indefinite integrals. Show your work a) S 5x* -+ b) f 3et ++ e dt dx

A: Here we have,  a) ∫5x4-3x2+25dx b) ∫3et+1e3t+e3dt

Q: Given the function graphed below, evaluate the definite integrals. 2 3 4 5 6 7 8 -3 -5 [²ƒ(z)dz = −5…

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Q: Every answer I get is wrong please explain the steps to me.

A: We are given indefinite integral.

Q: Activity 1: Practice makes perfect! Directions: Using FTOC, evaluate the following definite…

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Q: Evaluate the definite integral. 8. dx 3

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Q: Evaluate the following integrals, using integration techniques taught in this class. Writing the…

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Q: Evaluate the following definite or indefinite integrals (you MUST show all integration steps!):…

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Q: 2. Find the following definite and indefinite integrals. Use Substitution when needed a) f…

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Q: •V3 Evaluate (V3 – x? – 2|x|) dx by interpreting the integral geometrically.

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Q: Q3: Find the integral for the following functions: - 1 3)S sinh(x)-cosh(x) ax

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Q: (3) Evaluate the following indefinite and definite integrals: (a) ſ(x³ +e* )dx (b) 1 |dx + XVx -1 2…

A: We will evaluate the given integrals as shown below

Q: Evaluate the following integrals. You must show all steps to earn credit. x2 (a) V1 – dx. - x2 (b) /…

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Q: Q:: Find the integral for the following functions: - (* iS e3x .sinh(x) dx

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Q: Use a change of variables to evaluate the following definite integral. 6 S- dp /64 + p² 6 p | (Type…

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Q: 1+ cost 23. 14:Definite Integrals dt Answer:.

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Q: You need to evaluate the following integral: cos(ax?)dx Use four-point Gauss Quadrature to find this…

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Q: S sec?xdx Which of the following is the same as which will lead us to the correct evaluation of this…

A: We need to choose correct option.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.