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

Q: 2. xy dx dy

A: While integrating wrt 'x' we will keep 'y' as constant. While integrating wrt 'y' we will keep 'x'…

Q: Evaluate the iterated integral. 4z (In(x) xe- dy dx dz J3

A: Formulae used∫e-ydy = -e-y + C∫x2dx    = x33 + C ---------------------------------------- I…

Q: Evaluate the double integral : (y – 10x) dx | dy

A: we will integrate first inside the bracket with respect to x taking y as constant and then we will…

Q: S,(4y³ +-) dy y3.

A:

Q: Evaluate the triple iterated integral. 2/2 xyz dx dy dz 0/ -1

A:

Q: Evaluate the integral. dy y+2y-3

A:

Q: calculate the integral -2x+4 I=S (x2+1)(x-1)² -dx

A:

Q: 14 Find the integrals using integration by parts. a. fx(x + 4) dx c. fx'e"dx e flnx'dx d. [(In x)°…

A: (g) The given integral is, I=∫lnxxdx Rewrite as, I=∫xlnxdx Here, ∫udv=uv-∫vduu=lnx and du=1xdxdv=xdx…

Q: (x + y) dx dy Jo Jy/2

A:

Q: Evaluate the integral / (12x + 3y)dæ + (3x – y)dy along the parabolic arc y = x² from (0, 0) to (1,…

A:

Q: HiW 4i Solve the Pollowing Integral dy y-zy-3 16x3 dx 4火 -4X +1

A: According to our guideline we can answer only one question and rest can be reposted.

Q: Evaluate the integral (2x – y) dx + (x + 3y) dy along the path C. C: x-axis from (0, 0) to (0, -3)…

A:

Q: Evaluate the iterated integral. 2 1T 2 - 2y3) dx dy

A:

Q: Evaluate the double integral : (x + 2y – 4) dy dr

A:

Q: Use double integral to find the average temperature of T(x. y) = 10-8r -2y

A: Temperature function is given as - Tx, y = 10-8x2-2y2Average temperature = ∬10-8x2-2y2dxdyGiven…

Q: Evaluate the iterated integral. 74 (x² - 2y²) dx dy

A: Given that a double integral we solve this integration by using general property of integration.…

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 triple iterated integral. 2 xyz dx dy dz -1

A: We have to solve the triple integral.

Q: dv Integrate ду 1 partially with respect to y. II

A: To partially integrate the given function with respect to y, implies x will be treated as a constant

Q: Evaluate the triple iterated integral. ..* 2 Xyz' dx dy dz -1

A:

Q: Evaluate the double integral. y dy dx O - 3x

A:

Q: Evaluate the integrals ∫cos (1 - ln y)/y dy

A: We have to find the integrals: ∫cos1-lnyydy We will find this integrals by substitution method Let…

Q: Calculate the iterated integral. 2 (6 7e* + 3y dx dy

A: From the given problem: I=∫02∫067ex+3ydxdy So, we can also write as: I=∫02∫067ex·e3ydxdy

Q: Evaluate the iterated integral. (3x + 4y3) dx dy

A:

Q: In evaluating, 2x cos (2x) dx using integration by parts, identify the portion of the integrand to…

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

Q: Evaluate the double integral : (y° – 10x) dx| dy

A:

Q: Evaluate the integral / (10x + 15y)dx + (18x – y)dy along the paraboli - arc y = x² from (0,0) to…

A:

Q: Reduce to first order and solve. (1 - x2 )y" - 2xy' + 2y = 0, y1 = x. Use : fp dx = In [1/(1- x²)] ,…

A:

Q: 1. Sketch the region corresponding to the double integral •2 x+2 dy dx -1 Jx² and reverse the order…

A: A cartesian coordinate system contains two mutually perpendicular number lines named x-axis and…

Q: Evaluate the iterated integral.

A: The given integral is ∫01∫0y6x+5y3dxdy

Q: Evaluate the double integral : 9. dy dx 0, 22

A:

Q: 1. Sketch the region corresponding to the double integral rx+2 dy dx x2 and reverse the order of…

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

Q: Calculate the iterated integral x² ,3 sin x dy dx.

A:

Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the 10 cos t, y in (0 <t: curve C: x =…

A: A detailed solution is given below.

Q: Evaluate the double integral. (x - y) dy dx (x + y)3

A: To compute the double integral, ∬f(x,y)dydx, first integrate the function with respect y, while…

Q: Evaluate the iterated integral of 2 2x . (x2 + 2y) dy dx

A: Evaluate the double integral

Q: Calculate the iterated integral.

A: To calculate the iterated integral ∫05∫142xy4+3dydx

Q: Evaluate the line integral. -y dx + x dy segment from (3, 0) to (0, 3) x2 + y2

A: Find the slope of the line through the given points.

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

A: Given problem:-

Q: x³e-x*dx 1. "Since the integral ( Select ] [ Select ]

A:

Q: Evaluate the integral. /9-x2 dy dx dz = /9-x2 (x² + y²)!/2 3 J

A: Straightway, without any further delay, please convert to cylindrical coordinates: x = rcost; y =…

Q: Suppose we perform the substitution u=1+Vx in the integral dx . (1+Vx)5 What is the resulting…

A:

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

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

Q: Evaluate the integral (i) S3x3 sin 4x dx (ii) ſ In (x³ + x) dx (ii) cot-1 2x dx (iv) ſeax cos bx dx

A:

Q: Evaluate the iterated integral. (x2 - 8y2) dx dy

A:

Q: Solve the problem. Rewrite the integral 5(1 - z/6) 2(1- y/5 - z/6) dx dy dz in the order dz dy dx.

A:

Q: Evaluate the integrals 1 (x² + y² + z²) dz dy dx 0, 0,

A: The value of the integral is, 1. The detailed solution is as follows below:

Q: 5. Find the particular integral of d²y + dy - x2 + 2x + 4 dx2 dx

A: We use the operator method to find the particular integral of the given differential equation.

Q: Calculate the integral, for y> 2. 'Y x² - 4x + 5 √₂ - (x² − 2x + 2) (x² − 1) dx,

A: