8. Depending on the real parameter p and q, what can you say about the result of the following im- proper integrals r+oo 1 dx = lim xP 1 dx and dx = lim t0+ J x4 dx?

Q: Evaluate the iterated double integral: x+4 sin (y³ – 3y?) dy dx

A: Given: ∫-40∫x+42x+4siny3-3y2dydx To do: Evaluate the given double integral.

Q: 10 Suppose that " fx) dx and Ax) dx = -5, and "g(x) dx = -1 and g(x) dx = 3. Compute the given…

A: Given,∫04f(x)dx=7∫02f(x)dx=-5∫04g(x)dx=-1∫02g(x)dx=3

Q: 1 1-xl-x²-y? Evaluate the integral S S [dz dx dy 0 0 0

A: We will evaluate the given integral in this question.

Q: 2. Calculate the following integral: dx (a) sinh? x – 4 sinh x cosh x + 9 cosh² x +*) u (1– x²)² x…

A: 2) a)

Q: 23) Evaluate triple integral S dz dy dx. x-y

A: Given integral is ∫02∫x22∫x-yx+ydzdydx

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

A: Given integral is not an improper integral.

Q: 1 Suppose we perform the substitution u=3+Vx in the integral dx . I (3+ Vx)4 What is the resulting…

A: we have to find the given integral

Q: 14 Find the integrals using integration by parts. b. JF In /rdx In a. fx(x + 4)°dx c. fr'e"dx d.…

A: Just multiply by 1and go ahead.

Q: 3 2(x²+1)7 Write down an integral that gives the ARCLENGTH of y on the interval from x = 0 to x = 2…

A:

Q: 7. Express the solution of y" + 2y' + 2y = sin (3t) convolution integral (you don't need to evaluate…

A:

Q: 3 2 Evaluate the iterated integral x cos y dy dx. 2 3л 2

A: Ans= 5/2=2.5 For detail go through the solution...I have solved step by step in detail

Q: Q.3 Find the double integral for Sle x² dydx, where R between y = -4/x y = -x and x = -4

A:

Q: 1. In this problem, we will consider two methods that will allow us to evaluate integrals of the…

A:

Q: (4)Evaluate the definite integral (a)[ 1+sin x dx (b) | 2t + cost dt -7/2 5 x + dx (d)[ sec' 0 d0…

A:

Q: 2. Identify which of the following integrals are improper: 1 1 dx 1 fin(x)dx 1 X +3 1 fe* dr -dp- 3

A:

Q: 1. What should be A for the path independent of (2,4) xy + A 2Лу — х dy y? -dx + (1,2) Moreover…

A:

Q: 3 The triple integral L (x + 2y – z)dxdydz is equal to

A:

Q: Evaluate the iterated integral. 21 4 (x2 – 2y2) dx dy

A: We need to evaluate the following iterated integral ∫12∫04x2-2y2dxdy

Q: Evaluate the iterated double integral √1-x² _L [ ³²-x² sin (x² + y²) dz dy dx

A:

Q: Consider the following two improper integrals: (1) 1 dx г — 5 -1.7 dx (2) (x –

A:

Q: Solve the integral (5x - y)dx + (2x + cy)dy along the curves x = y3 from (0,0) to (1,1)

A: Explained below

Q: 22. To determine [x Inx dx pick the strategy that could work. a. A rewriting of the integral to fx*…

A:

Q: 0; x 0

A:

Q: Find a particular integral for y" + y' + y = 2 + x + cos x

A:

Q: If 9. 3. 6. f(x)dx = || f(x)dz + 6. what are the bounds of integration for the first integral?…

A:

Q: 14 Find the integrals using integration by parts. xp_ († +x)xf • - dx c. fr'e"de e flnx'de d. f (in…

A: Solution: The objective is to find the value of the given integral

Q: 2 1 Evaluate the iterated integral: y sin(Tx) dx dy 1 Jo

A: first we integrate the integtal with respect to x therefore integrate with respect to y.

Q: 15. Evaluate the given integral, V4 – 9x² dx: arc sin () A. x V4-9x2 2 arc sin () x V4–9x² В. + c 2…

A: Giiven: To evaluate the integral∫4-9x2 dxFormula: ∫a2-x2 dx=x2a2-x2+a22 sin-1xa+c

Q: Evaluate the iterated integral. 4 5 6 (x² + y² + z²) dx dy dz -4 0 0 5 6 (x + y? + 2? )dx dy dz = i…

A:

Q: L x(1 – 2r*)° dx

A:

Q: I. Evaluate the following integrals. Check by differentiation. 1. S(3x* + x2 – 10x + 6) dx 2. S 3x(x…

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

Q: 1. Set up the following improper integrals by definition. sin(x) dx 22 — За — 4 а. xe dx с. 4 et b.…

A:

Q: 3 9-x 9-x2 Evaluate the integral dz dy dx. 0 0 . 0

A:

Q: 1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de…

A:

Q: Evaluate the iterated double integral: x+4 sin (y – 3y?) dy d.x x+4

A:

Q: 39. Use a software application to compute the integrals у — х dx dy (x + y)³ у — х dy dx Jo (x + y)³…

A:

Q: 1. What should be for the path independent of (2,4) 2Ay – x dp. y? xy + A dx + (1,2) Moreover…

A:

Q: 2. Using an appropriate method, compute the following integrals. dx x² + 3x + 2 (i) sin³x cos*x dx…

A: (i)

Q: 1. Evaluate the integrals below. 5x²-x +3 (a) J x³ + x (b) [√v √√√x – 1 dx dx

A:

Q: Depending on the real parameter p and q, what can you say about the result of the following im-…

A:

Q: 4. Determine the following indefinite integrals: a) S(2x + 3x -7x2 + x-5) dx %3| b) S(x – 5)² dx g)…

A:

Q: (3) Evaluate the iterated integral , " (3 + x² +v²) dx dy.

A: First integrating with respect to x and then with y

Q: 3 5. Evaluate the iterated integral: S x(x² + y)'/² dx dy.

A:

Q: Apply trapezoidal and Simpson's rules to the integral 1 =[ \1-x² dx h=0,2

A:

Q: Consider the following boundary-value problem: du - sin Tx ; 0 < x < 1 dx2 subjected to the boundary…

A:

Q: Depending on the real parameter p and q, what can you say about the result of the following im-…

A: a ∫1+∞1xpdx=limt→+∞ ∫1t1xpdx     =limt→+∞ x1-p1-p1t   =11-p limt→+∞ t1-p-1   =11-p∞  =∞

Q: 2 Evaluate the iterated integrals. 2 (x + 3) dy dx 0, 6. y sin x dy dx

A:

Q: Find a formula involving integrals for a particular solution of D.E y" + 3y" – y' – 3 y = tan x

A: In this question, we find the particular solution of the differential equation. Here, we used the…

Q: 3. Which antiderivative of y = (1 – x²)-1 should we use to evaluate the integral (1 – x²)-' dx?

A: