Substitution in the Indefinite Integral Part 1. Using the substitution: u = 10z² + 3z – 6. Re-write the indefinite integral then evaluate in terms of u- Note: answer should be in terms of u only Part 2. Back substituting in the antiderivative you found in Part 1. above we have (2z 10z+3z-6 Note: answer should be in terms of I only

Q: 2(x° + xy* + v)dx + (2x°y³ + 4xy° + 2x°y + x*y +2x)dy = 0: y(2) = 0 3.

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Q: x(x (x X),Xx

A: We are asked to evaluate the integral.

Q: Agree. Disagree 5. If lim f(x) # lim f(x), then lim f(x) does not exist. Justify:

A: Let's find. 

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A: Given that:                          

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A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost oth...

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A: The given curves are:   y=x     and     y=-x

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A: Solution is here

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Q: Sss*dx= [s 521²dx 5'52 dx A True B False

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Q: yesin 3y* dy dy 5. csc 6y

A: The question is a little incorrect. I have modified the question a bit: the denominator should be: c...

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Q: . (6xy² – xey + 2y)dy = y(e*y – 2y²)dx

A: Using method of exact differential equation.

Q: d the area (sq. units) covered by the line 2y = x + 6 from x1 = -8 to x2 = 0.

A: Given query is to find the area bounded by the curve.

Q: Find the nearest degree the directing angles of b = -i +3/2j+1/3k

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Q: Integrate the rational function by partial fraction (decomposition): 2-9-dx r3-9x

A: Let I=∫x2-9x-9x3-9xdxApply the Sum Rule:  ∫fx±gxdx=∫fxdx±∫gxdxI=∫x2x3-9xdx-∫9xx3-9xdx-∫9x3-9xdxI=∫x2...

Q: EVALUATE THE INTEGRAL OF THE FOLLOWING. INDEFINITE INTEGRALS. CLEAR

A: We will find the integral's value. 

Q: cotxdx + ysin?xdy = 0 %3D

A: Using variable separable method.

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A: The given function is: f(x)=5x+87x+7

Q: 1. y'dx-(xy+ y° kdy = 0 Let the substitution y=2; y= vx; dy=vdx+ xdv

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Q: Center of Mass: Thin plate (region in the plane). Suppose Ris the region bounded by the graph of f(z...

A: We need to find center of mass.

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Q: x'dy +(2xy – y* kdx =0 2. Let the substitution y =2 y = vx, dy=vdx+ xdv

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Q: Find the centroid of the region bounded by the gi 1 y = 0, x = 1,x = 3 %3D %3D

A: Given:y=1/x ,y=0 ,x=1 and x=3 Find: the centroid of the region bounded by given curves.

Q: Determine the values of x for which the given function is undefined. (Let k be any integer.) y = co...

A: To determine the values of x for which the given function is undefined. y = cot x 

Q: 3. sinx tan x + cos x

A: We can simplify the expression as below.

Q: What is the period of G(x) = 5 sin(3x - 3 T)? %3D 2pi 2pi/3 2pi/5

A: Given that: G(x)=5sin(3x-3π)

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A: Given: y=x3, y=1, x=0 & x=1 From the given curve the bounded region is as shown below: Apply th...

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Q: The demand for a new computer game can be modeled by p(x) = 57 -7 Inx. for 0sxS 800, where p(x) is t...

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Q: Agree. function always exist? Justify: Disagree 2. Does the limit of a

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Q: 2. x'dy+(2ty– y°l&x =0 Let the substitution y=²; y=vx; dy=vdx+ xdv

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Q: What have you learned in evaluating integrals?

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Q: Solve the homogenous equation. 1. y'dx-(xy+ y³ \dy = 0 Let the substitution y=²; y=vx; dy=vdx + xdv ...

A: Substitute v = yx and solve the given differential equation. Note : As per our Guidelines , we can s...

Q: general function M(x, y) or N(x, y) so that equation is exact.

A: We will find the function (general). 

Q: Consider the series > 5e". n=0 a. The general formula for the sum of the first n terms is Sn (5e( 1-...

A: This is a problem related to series calculation. Based on the simplified terms it was observed that ...

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

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Q: x'dy+(2xy – y² )dx = 0 Let the substitution y= y=vx; dy= vdx + xdv

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Q: A circular swimming pool has a diameter of 8 meters. The sides are 4 meters high and the depth of th...

A: Using fluid concept

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Q: On the domain of (-27, 27), for which of the following values of x will sin x = csc x? Choose all an...

A: Our Aim is to find the following values of x which satisfy sin (x)=csc (x)on the domain of -2π, 2π.

Q: II. Solve the following homogeneous differential equations. 1. y'dx-(xy+ y kdy = 0 Let the substitut...

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Q: The period of y = 3 cos 5x is 2 2 /5 2 /3

A: Given that: y=3cos5x

Q: The period of y = 3 cos 5x is 2 TI 2 T1/5 2 π/3

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Q: (I-) = 2- VT-I (b) i) Compute lim- ii) Hence prove the limit in i) above by -ố definition. 2

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