Evaluate each of the following line integrals. Sc [(x² - y2)dx + (2xz)dy + (xy-yz)dz] where C: x = 2t - 1, y = t +1, Z= t-2, 0≤t≤ 3.

Q: Question 21 dx Evaluate: S (x+1) log(x+1) (A) In 10 log² (x + 1) + C 2 B In[log(x+1)] +C In 10 C…

A: We need to evaluate integral.

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: To evaluate the integral. Option A is correct.

Q: Which of the following is NOT a method for finding volume of solids of revolution? A conic method B…

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Q: Which integral below gives the volume of the solid of revolution obtained by rotating the bounded…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 1 A -unit² (B) unit² 1 H|m

A: Given that fx=x+13  and gx=x+1Solution :x+13=x+1x+13-x+1=0x+1x+12-1=0x+1=0 and x+12-1=0x=-1 and…

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: Find the are bounded by the curve y = x and y = x^2 - 2. * 2/9 sq unit 9/2 sq. units 16/3 sq. units…

A: Use the intersection of the curve and then integrate the upper curve minuses the lower curve to find…

Q: [_²_f(x) dx = 0 and [ f(x)dx = 11₁ Given 6 A 0 B C D 11 5 11 6 55 6 evaluate 1 [²3f(x) dx - √₁2 f(x)…

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Q: Question 32 Solve the integral: A) 3√√√x² +C (B) ex 3 2√x² +C с D 6√√x +C 3√x x² dx

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0? A) none B) 1 infinitely…

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Q: Question We can apply General Power Formula of Integration on which of the following integrals? A…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: dx S secx + 1 1+z² Ⓒ √ 1+ 2²/ dz S A 1-z² -z² B 1+z² © √²/²+²/d² S³ -dz 1-z² 2-2z² / 1²= D 1+z²…

A: Note: According to our expert guidelines only first individual question is to be answered kindly…

Q: Evaluate the double integral: A) 80 B) 30 C 60 D 40 √²² (3x² +9y²) dxdy 0 0

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0? A may vary depending on…

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Q: The function is x z = y² What is 8²% dy² 2/21/23

A: Let's find second partial derivative of given function.

Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

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Q: x²+3x-7 X-2 +5x+31n|x-2|+C + +In|3x-6|+C 2 x²+5x+In/3x-6|+C x² + 5x + n/x-21 +C 2 3 In Evaluate the…

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Q: Determine the area bounded by f(x)=x2-x and x-axis. A — -unit² 2 B Ⓒ с D 16 unit² -unit² -unit²

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Q: tanx If f (x) = A (В) (ⒸC) D - St 0 sec 3x 1+ e tanx In (secx) √ 1+tan ²x 1+ e tanx sec²x 1+elanx…

A: Finding the derivative of the integral

Q: Determine the area bounded by the functions f(x)=(x + 1)3 and g(x)=x+1,

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Q: B S₁ Evaluate: A In 10 (В) ® -log² (x+1)+C 2 In 10 In[log(x+1)] + C -In 10 log2 (x+1)+C 2 D dx (x+1)…

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Q: y = Arctan ( 2+x 1-2x

A: The derivative are

Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, the limits of…

A: In this question, we want to know the limits of the Integral as a horizontal element.

Q: 5. (D²+4)y=4 cot 2x

A: We use variation of parameters method to solve the given differential equation.

Q: Evaluate the integral: e3+ cosh2x33+ cosh2xsinh2x dx

A: We know that integration of ex is ex + c .     Here i attached the solution of this question.

Q: +3x-4)³ (4x+3)dx + C Solve the integral: Seln(2x²+3 (2x²+3x+4)*(4) A 3 (2x²+3x+4)4 4 eln(2x²+3x-4)³…

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Q: ·S A B If D A (x+2)(x-1)² = √2 + x + 1 2 9 3 9 -la 1 I 2 93 1 9 2 9 3 . 2|3 B x-1 + C (x-1)2 (x -…

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Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: Let f(x)=√√3x-2 on the interval volume of the resulting solid. 83л A -unit 3 125 43л 135 43л 125 83л…

A: Let's find volume of resulting solid.

Q: S Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

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Q: (x + 1) dx (x+2)(x-1)² 15 S= = √ [ +42 A B + x + 2 x-1 C + + (x-1)2]dx. dx, the values of A & C…

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Q: S 1 Solve the integral: √√√X = n/1+x²³²|+c A C {/in/1+x²³ | +c B © 6n/5+x²³²|+c C in/1+x³| +c D X +…

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Q: Which of the following can be determined given (A) L²³ F(x (f(x) + g(x) +h(x))dx g(x) dx © L² F…

A: We can solve this as follows:

Q: Determine the area bounded by f(x)=x²-x and x-axis. A unit² -unit2 unit² |+ B 2 © ½ u Ⓒ / unit ² D…

A: Let's find area of given curve.

Q: Find the area bounded by : f(x)=e*, g(x)=e* and x=3. A (e²-1)² e2 sq. units (e³ + 1)² e3 (e²+ 1)² e²…

A: Given:-the region bounded byf(x)=ex, g(x)=e-xand x=3

Q: Determine the area bounded by the functions f(x) = (x + 1)3³ and g(x)=x+1₁ A unit² B unit² 3 Ⓒunit²…

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Q: Which of these expressions represents the area between the curves y = x^2 and y = 6 - x from X = 0…

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Q: Evaluating (A) (B S -3 of */2 si 57/2 18 18 ofth 0 (D) 9-x² dx using trigonometric substitution will…

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Q: Evaluate the triple integral: 3 ₂2 0 (x+y+z)dydxdz

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Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: Evaluate

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Q: HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. (D3 – 6D2 + 12D – 8)y = 0

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Q: Find the area bounded by: f(x)=e*, g(x)=ex and x = 3. A (e³-1)2 e3 sq. units (e²-1)² e² sq. units…

A: Please see the below picture for detailed solution.

Q: The improper integral A 1 B 0 C St edx is

A: To solve the improper integration.

Q: If f(x) = A B C D tanx S 0 sec²x √1+1² 1+e¹ -dt, then f'(x) equals 1+e tanx In (secx)√1+tan²x 1+ e…

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Q: 1 √√√√√x+x X Solve the integral: S- @ =√² m/1 + x ²³ / + c A C (1) 6in/5+ x ³²³| +C B © ²/³ m/1 + x…

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Q: Stan² √I+1² 0 l+e' 1+tan²x tanx 1+e In (secx)√1+tan²x 1+et tanx sec²x 1+elanx sec 3x If f(x) = A B…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: The correct answer is option (c).

Q: The function is x % = y? What is 8 2 dude Y æ2

A: We need to find derivative.

Q: That statement "We can use the General Power Formula of Integration for indefinite integrals…

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