Evaluate the following * [: 2x(4x² – 3)³dx (4x²-3)6 +C 24 O (4x² - 3)-6 24 +C (4x²-3)6 24 O " (4x² - 3)5 24 + C +C

Q: Find the area of the region bounded by the curves 1 y= (x+6)²¹ y = 4 and the x-axis using vertical…

A:

Q: Determine the equation for the line with normal vector n = [3,-4] passing through the point P(-1,-2)

A: Given.

Q: -2 Evaluate: ²₁²[(x²-²²] 0 x+y du dt

A: Topic = Integration

Q: An integrating factor for the linear differential equation y' + = x is Select the correct answer. O…

A: This question can be solved using the concept of linear differential equation. Note: elna=a

Q: Solve for C using the form f(x,y)=C. Given [2x + ycos(xy)] dx + x cos(xy)dy = 0; f(1)-pi/6. decimal…

A: differential equation

Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ y = 4 and the x-axis using vertical…

A:

Q: xn+xn-1+xn-2+...+ roo (n−1)n-1+(n−2)æn=2+…+ What is the lim ne Zt?

A: This is a problem related to limit and continuity. Based on the general formula and concept we will…

Q: 2. Evaluate all of the integrals. [ 2² sin sin a dr

A:

Q: 3 Evaluate: ₂(4x²y - z³) dz dy dx

A:

Q: he table of integrals to evaluate the integral. (Use C for the constant of integration.) sin (20) J…

A: The solution is given below.

Q: Two passenger airplanes left the same terminal at the same time. One plane flew due north at an…

A:

Q: Evaluate: ₁³(x + y)³] dz dy dx S²³₁

A: A detailed solution is given below.

Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

A:

Q: b. Two passenger airplanes left the same terminal at the same time. One plane flew due north at an…

A:

Q: Evaluate the limit using L'Hôpital's Rule. 8x³ lim x-0 sin(x) - x (Use symbols and fractions where…

A: we want to determine the value of limit limx→0 8x3sinx -x

Q: Evaluate the indefinite integral given below. (10 (10-20x4) csc² (2x³ - 5x) dx

A:

Q: Evaluate the integral: -2е π/3 ƒºƒ²² ƒ”¹/³ t ln u tans ds du dt see

A: Given

Q: II. Evaluate the following integrals. -3 3. √²* |2 - 2ª | dx 0 c

A:

Q: Determine the instantaneous rate of change of the function √ sin sin (2³) f(x) = [x² x3 At x=1 dt…

A:

Q: What will be the orientation of the curve of the graph of the function f(x) = on (-3,0)? A.…

A:

Q: Evaluate the following limit, if it exists: lim x->7 = √x + 2 - 3 / x-7 (The square root covers…

A: In this question, we will evaluate the given limit expression.

Q: Explain why the equation 7 = (-1,0, -1) + s(2,3,-4) + t(4,6,-8) where s, t ER does not represent the…

A:

Q: r²[(x²-y²)²] 1²₂5²² du dt x+y

A:

Q: Evaluate the integral: S2 S² sin (=) dt du π/2

A:

Q: If lim f(x) = -∞, then which of the following is TRUE? I-0 O None of these. Ox= = 0 is a vertical…

A:

Q: -3 Evaluate: ²¹²² ²³ y cos(z³) dx dy dz

A:

Q: Ex. Find the general solution to dy 1 -2.x dx X -

A:

Q: Evaluate the integral: ² ls teu du ds dt 0

A: We need to evaluate the following triple integral ∫12∫tt2∫0lnsteudu ds dt

Q: dy Exercise 1.7.7: Consider =yx², y(0) = 1. dx a) Use Runge-Kutta (see above) with step sizes h = 1…

A: Since you have asked to solve multiple questions. As per our guidelines we are supposed to answer…

Q: Evaluate: ³₁² [(x² - y²) ² x+y 21 du dt

A: The integration of the double integral is  (x2-y2)2/(x+y)

Q: 7)(x+tan y) dy sin 2y dx

A:

Q: t√√t + ,2 + t dx

A:

Q: IV. A small business determined that the price-demand and cost functions for producing and selling x…

A:

Q: Evaluate the integral: -2e 2е π/3 ₁² /³ tlnu tans ds du dt 0

A: In this triple integral we first integrate with respect to 's' then with respect to 'u' and in last…

Q: Q2/ Find the derivative 1. sin(xy)= of each of the following functions:- 2. y =(Inx)³ 3. y=cos (sin…

A:

Q: Find the area of the region bounded by 2x and the y-axis using the horizontal strip. 3 y² +1

A:

Q: S √x²-25 dx X

A:

Q: Find ди ds if w = sin(xyz), x = 1 - 3t, y=e¹-t, and z = 4t, find o

A:

Q: cln s Evaluate the integral: St² főr teu du ds dt

A:

Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

A: We have to find the volume of solid generated by revolving the region bounded by 2y = e-(x^2) , the…

Q: !

A: Please refer to the image below

Q: Use the table of integrals to evaluate the integral. 2 √2²47x²³ √4x²-x+ d² dx

A:

Q: slope

A: Please refer to the image below

Q: y' = xy2 O y(x? + c) -2=0 2 (x² + y=(x+ c) + 2 = 0 y(x= + c) + 2 = 0 y2(x? + c) + 2 = 0 00 Ꮎ

A:

Q: Find the area of the region bounded by 2x = and the y-axis using the horizontal strip. 4 y²+1

A: We have to find the area using horizontal strip.

Q: 1. Given vector 2 0-3 is 2. It is known that a à vector : ( 2 ) and 3 = (-1) is a vector in 1R³ with…

A:

Q: Find the total area between the graph of the function f(x) = x + 1, graphed below, and the x-axis…

A:

Q: I. Evaluate the following limits. 2 2. lim (x - Inx)* x→0+

A:

Q: (x - 1)ex (x + 1)³ -dx

A:

Q: For the following exercises, use the second derivative test to identify any critical points and…

A: Given :f(x,y)=-x2-5y2+10x-30y-62