Find the volume of the solid obtained by rotating the region bounded by y = 7x², x = = 1, and y = 0, about the x-axis. V =

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Q: INTEGRATE THE FOLLOWING (use integration techniques) -2y dy 2. Sy'e-24 dy

A: topic- indefinite integral

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A: F(s)=3s(s2-2s+s)F(s)=3s(s2-s)F(s)=3s2(s-1)Partial fraction:3s2(s-1)=As+Bs2+C(s-1)3=s(s-1)A+B(s-1)+Cs...

Q: (a) f(x)= Jx-6 (b) g(x)= /7-x (c) h(x)=V1-x²

A: Since you have posted multiple questions in this question which are not interlinked so I have solved...

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A: Let's find. 

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A: Given query is to find the derivative of the expression.

Q: Find tue indefinike insegred. Jcostex) sin'ces) de 3 6 (os (2x) Sin

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Q: Qal AIf fo =Sx-ul, gca)=x fin d fogcx) Then graph it determine domain and range.

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: Consider

A: Please refer to the image below

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Q: 3х - 4 dx Evaluate the definite integral. Give exact answer

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Q: 6) pind ful indefinite integrel. 4 sec (2x) de

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A: This question is based on solution of differential equation.

Q: / V16 – x² dx, we use Select one: O x = 4 sec 0 O x = 4 sin 0 O x = 3 sin 0 O x = 3 tan 0 O None of ...

A: The integration of the integral is√(16-x2).

Q: substitution x = tan 0, then, the integral dx 1 + x2 transforms into tan 0 sec 0 d0 Select one:

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Q: 2 V = 5500 find (1- 50 0<t< 50 the cate which water drains at tme (rate must be nesative).

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Q: any method to determine if the series converges or diverges. Give reasons for your answer. 00 3 3 Σ ...

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Q: What Mclaurin Series this function represents: En=1(-1)n+1 =" = ¤ n 3 O a. In(1+x) b. cosx c. sinx O...

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Q: ( 2 + x², -2 <x< 0 4 f(x)dx; f(x) = 1 ·x + 2, 1. 0<x< 4 -2

A: ∫ xn dx = xn+1n+1 +C ∫ab f(x) dx = ∫ac f(x) dx + ∫cb f(x) dx , where , a&lt;c&lt;b.

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y ...

A:

Q: 1. Evaluate the line integral I = = [v¢4x° + y*) dx + x(2x° + 3y*) dy] around the ellipse x/a? + y/b...

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Q: Suppose f(x) and f'(x) have the values shov 33 34 35 36 37 f(x) f'(x) 9 17 5 4 15 3 -4 -3 -5 -2 1 Le...

A: We will find the value of the function. 

Q: A water tank in the shape of an inverted circular cone has a base radius of 4 m and height of 6 m. I...

A: A water tank in the shape of an inverted circular cone has a base radius of 4mand height of 6 m. If ...

Q: 8. y = In(x + Vx² +1)

A: According to given, only 8 is solved  

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A: According to the problem, we have

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Q: If x + y = 0 and x # 0, then what is the value of x 2007 y 2007 O -1 O 2 O 1

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Q: X X sin². sin? - cos' ,dx CoS 2 2 2.

A: x2=u → dx=2 duI=2 ∫ sin2u cos7u duI=2 ∫ sin2u cos u cos6u duI=2 ∫ -sin2u cos u (sin2u-1)3 dusin u =v...

Q: 3. Consider the following surface and the point Pon the surface. Let C'be the path of steepest desce...

A: f(x, y)=y3 - x2∇f =fx, fy =-2x, 3y2Descent = -∇f =2x, -3y2This can be put as;that the slope of the d...

Q: Let f(æ) = (4x² + 5æ + 2)° f'(x) =

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Q: True or False; In the partial fraction decomposition, x + 8 A В D + x(x – 1)(x + 3) х — 1 x + 3 - we...

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Q: 7. Find the volume of the solid formed when the graph of the region bounded by y = e, x = 0, x = 2, ...

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Q: Evaluate the given integrals. sin 6x dx sin23x 4.

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Q: Find the equations of planes that just touch the sphere (x – 5)2 + (y – 3)² + (z – 5)² = 9 and are p...

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Q: After some thought, you have decided that you will need $60,000 each year to live on after you retir...

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Q: S 12x²Vx3 + 7dx

A: This question can be solved using the concept of integration by substitution.

Q: 5 Find the lateral (side) surface area of the cone generated by revolving the line segment y = x, 0s...

A: If the curve y = f(x) , a≤x≤b is rotated about x-axis, then the lateral surface area is given by    ...

Q: 2 + x², -2 < x < 0 f(x)dx; f(x) TX + 2, 0<x<4 21 -2

A:

Q: 8. Use the two-column proof table to simplify the given proposition. PV {¬(-Qv P) A-(-QVP) v (Q A¬P)...

A: Using table solve it. 

Q: List the eigenvalues of A. The transformation x-Ax is the composition of a rotation and a scaling Gi...

A: