1. Which of the following integrals is improper? Explain your answer, but do not evaluate the integral. dx х0.2 (b) -x dx 00 (a) dx (c) x!/3 (e) 00 (d) sec x dx (f) sin x dx e-* dx sin x dx (h) lo V3—х2 (g) dx (i) In x dx (j) In x dx

Q: 7. If f is negative on [-3, 2], is the definite integral f(x) dx positive or negative? What about…

A: It is given that function f is negative on -3,2

Q: Q1- Express of the integral in term of Gamma function and simplify where possible *e-2 dx.

A: Gamma function

Q: how I calculate the definate integral 3x^2-e^2x(dx) on the interval ln3 to 0

A: To find the definite integral

Q: x dx = b2 - . T/2 cos(x) dx = 1, together with the properties of definite integrals, to evaluate…

A: To calculate the integral using the given formulae

Q: We have determined that du = 5x* dx. However, the given indefinite integral dx does not conta %3D x…

A:

Q: 3. Find the following definite integrals. (2x +3)dx (x2- 1)dx x² - 2x)dx sin(3x + 4) dx 1

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Q: Evaluate the integral: e³+cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 2In3 + C (3e)3+ sinh2x B 2 + In3…

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Q: 6. Evaluate the integral ex e* +e-xdx

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Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

Q: Evaluate the integral: Se3+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 - + C (3e)3 + cosh2x B…

A:

Q: 52. Use Property 8 to estimate the value of the integral 1 dx Jo 1 + x2

A: Given: Integration 0 to 2 of (1/1+x^2).dx

Q: Q1- Express of the integral in term of Gamma function and simplify * x*e-2x dx. where possible

A: Use gamma function

Q: 7. Evaluate the integral using integration by parts. S cos (5x)e 2* dx.

A: Given the integrationI=∫cos(5x)e2xdx

Q: 2 sinh x Calculate the integral, J dx. 5+ 6 cosh x

A: Given :∫2sinhx5+6coshxdx

Q: Given the definite integral, its limits are to be substituted to x³ dx x + 1 x² x² 2 x3 3 Option 1 +…

A: Given problem:-

Q: 3. Find the indefinite integral: Sx(x-2)* dx

A: Please rate

Q: A. Evaluate the following indefinite integrals using the Power Rule: 1. SE Va dx 2. S dx 3. S(-Vx +…

A:

Q: Evaluate the indefinite integral given below. 2e3 sin (4z) cos (4x) dx Provide your answer below:…

A:

Q: Evaluate the 2 improper integrals attached with this question.

A: Given integrals are

Q: 4) Use the Midpoint Rule to approximate the integral. Then evaluate the actual integral. L(3x - 7)²…

A:

Q: To apply the integral test for 3n2 + 1 n3 +n n=1 we evaluate the improper integral 0 3x2 + 1 dx. x3…

A: Solve the following

Q: What is the integral of ((x^2)*e^(3x))dx from 0 to 1?

A:

Q: 3. Evaluate the double integral /sin(x+y) dx dy by using Simpson's 1/3-rule with four sub-intervals.

A: I = ∫0π2∫0π2sin x+ydxdy,

Q: 4. What is the geometric relationship between the two integrals below? et dx, In x dx Evaluate the…

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Q: 6) Evaluate the improper integrals ∞ 5 a) 5² (+ + e-") dx s (-x) е 2 7 5 b) ² = 8 dx 4x-8 2

A:

Q: 2.2 (e-x* + 1) dx 0.5

A: Topic-integration

Q: Exatuate the integral pvz O√3 √4-X² √EX 9 (√x ² + y² dy dx

A: Evaluation of double integral by conversion to polar coordinates.

Q: (ii) Estimate the integral I 1.4 sinx-log.x+e*dx 02 by using trapezoidal rule with h=0.2 correct to…

A: We can solve using trapezoidal rule

Q: When using Simpson's rule to approximate the integral In(x+1)dx, then the upper bound of the error…

A: Consider the given information. I=∫23lnx+1dx Let's take 1 for n for the error bound. Calculate the…

Q: Estimate the value of integral 3 to 1 dx/x

A: Given,  ∫131xdx

Q: Step by step

A:

Q: Q1- Express of the integral in term of Gamma function and simplify where possible r°e-2x dx.

A:

Q: 4-Évaluate the following integrals a) In dx b) ] ()"- dx 5/2 tan x

A: Integration:   The collection of all antiderivatives of f is called indefinite integral of f with…

Q: 3. Apply Romberg quadrature to •1 1 dx 1+ x2 for h = 1, 1/2, 1/4, 1/8. Show a table of approximate…

A: We are given the following definite integral : ∫1/(1+x2) dx from 0 to 1 And we have to solve it…

Q: 7. Integrate the following indefinite integrals. 3e5x dx 1-2e5x a.

A:

Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

A:

Q: 4) Evaluate the following indefinite integrals. a. S (+ V3 - dx 4 3x2 b. S (2 sec2 x- 5 cscx cot…

A: Integrare

Q: 4. Determine the following indefinite integrals: a) S(2x* + 3x³3 – 7x² + x – 5) dx b) S(x – 5)² dx •…

A: 4. Power rule of integration states that: ∫xndx=xn+1n+1 (a)To evaluate the integral:…

Q: (2+ln² x) 2. S: -dx x(1-In x)

A: As per rules supposed to solve only one problem at a time so please post the remaining question as a…

Q: 1. Evaluate these integrals either by substitution or by integration by parts: cln 2 et a sin(2r) dr…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2 S sin (ax)cos(ax)dx

A:

Q: 1) Evaluate. Јx cosh ax dx 2) Evaluate the integral. (In x)² dx x3 1

A:

Q: 3. Find the value of c guaranteed by the MVT for integrals for f(x) = cos(x), [-; 3'3 ] over this…

A: f(x)= cosx  , [ -π3,π3]as per MVT for Integrals for a function f(x) bounded and integrable on [a,b],…

Q: If the integral of /x + 1 dx from x = 0 to x = y is equal to 14/3 , what is y?

A: Substitution Method is used

Q: 46) Estimate the minimum number of subintervals needed to approximate the integral T/2 6 sin x dx…

A: Find the minimum number of Subintervals.

Q: Which of the following integrals are improper? (Select 3 L₁x²-1 dx 3x - 1 1 06²/21 x ² = 1 dx 2x 00…

A: Topic:-  improper integration

Q: Calculate the integral approximation S6 for 2 2-a" dx. 1 S6

A:

Q: 2 Evaluate the improper integral e4z dx, if exists. a) The nature of the integral is:

A: Explanation of the solution is given below...

Q: Q1\ Evaluate the integrals: 10 A. S- V16+x2 В. Г(3 — 2х)-5 dx

A:

Q: 1. Evaluate the integrals that converge: dx 2x ! dx (x2 + 5)3 b) a) 3-x - 00

A: