Evaluate the following definite integral by the limit definition. | (3 x² +4)dx а. —9 b. 21 с. -21 d. –3 е. 9

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A: As per the guidelines, I can solve only first question. Kindly repost the question for second…

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A: According to the given information it is required to determine whether the integrals in each part…

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Q: Express lim E=1 Ax ||PI0 as a definite integral where P is a partition of [0,2]. k%3D1

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A: Here we use the substitution 4-x=u to solve this integration.

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A: Please see the answer below.

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A: Given Integral, I =∫01∫x3x2x5dydx Region of integration is, 0≤x≤1 ,x3≤y≤x2 Graphically the region of…

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Q: 1. Evaluate the following integral using the substitution u = 2x + 1: 15x/2x +1 dx HINT: Don't…

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Q: Define the following improper integrals integral - infinity to 0  f(x) dx

A: Given: The improper integrals f(x)dx from limit -infinity to zero.

Q: Given Rn 2 + i- cos ( 2 + i- express the limit as n → 0 as a definite integral, that is provide a, b…

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Q: e | 8y³ In(y) dy 1

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Q: Evaluate the following integral: 7 dx = 团+C 2 V2 – - 49 – 49 Note that an arbitrary constant has…

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Q: Determine the following indefinite integral. 1 dy 14y

A: To evaluate:   ∫114ydy Property of integration used, 1. ∫cfxdx=c∫fxdx                           …12.…

Q: I don't understant this hw problem

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Q: Which of the following integrals will find the length of the graph of f(x) = e* for 0 < x < 4? %3D

A: Given,          fx=e6x for 0≤x≤4.

Q: 1. Rewrite the following improper integrals as a limit and then evalute them, or state that they…

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Q: Evaluate the following integral by using substitution ∫4x/√(x^2+1) dx   limit: 0 to √48

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Q: dx C = 4r This integral is improper because of the infinite discontinuity at x = r, and hence we…

A: If the intregral is improper on a finite interval where the integrand is unbounded at the upper end…

Q: Evaluate the following definite integrals. 3. If f(x) = V19+f dt ,find f'(3).

A: We can solve as follows

Q: Evaluate the following indefinite integral. + 4/x dx + 4/x dx = ||| (Use C as the arbitrary…

A: Evaluate the given indefinite integral:

Q: Use the following property of the definite integral to estimate the definite integral: f/4 π/6 […

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Q: Evaluate the following definite integrals, t(1 -t)² dt = а.

A: Solution: ∫-11t(1-t)2dt Expand=∫-11t-2t2+t3dt

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A: Integration

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A: To evaluate the given limit

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Q: ܐܐ 19. dz 'z(nz5

A: The given definite integral is ∫122 dzzlnz1/5. Solve the definite integral by the substitution…

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A: According to the trapezoidal rule, the definite integral of a function fx over the interval a,b can…

Q: Which of the following definite integrals represents the limit: 1+ z?A¤ lim n00 You may use the fact…

A: Given:-limn→∞ ∑i=0nxi1+(xi)3 ∆x    on the interval 2, 5integral as limit of sum∫abf(x)dx=limn→∞…

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A: According to question given that (i)  ∫1∞1+sin2xxdx     (ii) ∫1∞x+1x4-xdx

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A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 4. Evaluate the following integral: S tan3 x dx

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A: Given: To evaluate the integral: ∫0∞sin(x) dx   Formula used: ∫0∞f(x) dx=lima→∞∫0af(x) dx

Q: -0.1x dx e 1 8.

A: We use integration of e^x dx =e^x.

Q: Which of the following correctly expresses the limit lim n00 n as a 1+ (i/n)2' definite integral? 1…

A: Given  : Limit limn→∞ 1n∑i=1n11+i/n2   To find : Write the given limits as definite integral?

Q: r1 x³ +1 dx x +1 Jo

A: Definite integrals can be computed using the fundamental theorem of calculus. It states that if…

Q: 2 s² +V5 ds 2.1 s2 V3 L(t + 1)(t2 + 4) dt 2.2

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Q: 1 dx. x+ v1+x

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Q: 2 Given Rn 2 + cos ( 2 + i- , express the limit as n → ∞ as a definite integral, that is provide a,…

A: To find the following terms in the integratiin given definition of integration.

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Q: 2. Evaluate the following integral: 6/ dx x2 Hint: Use x = 3 cose.

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Q: Evaluate the following integral or show that it is divergent. 0 -√x VX dx

A: Explanation of the answer is as follows

Q: Q5: Compute by part the following indefinite integral Sx. In x dx

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.