Evaluate: dx (x+1) log(x+1)

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

A: The integration are

Q: Let f(x)=√3x-2 the y-axis and find the volume of the resulting solid. 83 (A) -unit ³ 135 83 (B)…

A: We will draw the curve f(x) and y=1. Points of intersectionf(x)=3x-2   and y=11=3x-2 1=3x-2x=1Point…

Q: 5. (D²+4)y=4 cot 2x

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

Q: y = 3 Arcsec 3x

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Q: Find the area bounded by : f(x)=e*, g(x)=e* and x=3.

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Q: 2 Let f(x)=√3x-2 on the interval 1 1. Revolve the region between the curve, y=1 and y-axis about the…

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Q: In the indefinite Integral in(cosh x + e*)- A sinh xte cosh x + ex sinh x + ex In(cosh x + e*)…

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Q: Determine the area bounded by the functions f(x) = (x+1)³ and g(x)=x+1. 1 A unit² ® 2-unit² B 1…

A: Please see the below picture for detailed solution.

Q: Question 25 x + 2 Determine the case of the following proper rational function after simplification:…

A: We have to determine proper rational functions and choose correct options

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

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Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

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Q: How many antiderivatives does a function of the form f(x) = x^ have when n0? (A) 1 B) none (C)…

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Q: feschucoshudu cschusinhudu sinhucothudu cosh coshu sinhudu O fir

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

A: Given that g(x) is a differentiable function and range of g(x) is interval I. f(x) is a function…

Q: Q/IF 3 = sin(x) 0²³²141 y= (4) y = 3/2 I sin(x) cos(x) Prove that

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

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Q: van [ f(x)dx = 5, [_o(x)dx=7, and [_n(x) dx = - -5 Which of the following can be determined given…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: y 3 Arcsec 3x

A: Find out the y'.

Q: Determine the case of the following proper rational function after simplification: x + 2…

A: We have to find out simplification

Q: Evaluate

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Q: If $S₁ A B (x+1) dx (x+2)(x−1)² 9 3 D -la 1 9 I -ja 2 3 2 93 12 93 ==√ [= ²4/2+1 B x-1 C (x-1)² ]dx…

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Q: (x+1)dx (x+2)(x-1)² 1 / S If B -√2-1 + + *(x-1)2 ]dx. +2 dx, the values of A & C respectively are:

A: We can solve this as follows:

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

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Q: Given A) B (C) D 11 √ √ ² f(x) dx = = /10 f(x) dx = 0 and 11 6 20 55 •[ 37/(x)dx - 5² 2/(x)dx…

A: D option is correct.

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: The limits of integration will be the interval on the x-axis for which the area is bounded.

Q: e integral be 'solvable' using trigonometric substitution. What is the correct choice of u given J…

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Q: 19 Let u(x) = sin(x) and v(x) = x¹9 and f(x) = u'(x) = v'(x) = u'v - uv' f' 2² u(x) v(x)

A: sin(x)' = cos(x) dxndx=n.xn-1

Q: Question 5 The improper integral A e B) 0 (C) D 1 8 +∞0 Se ex dx is

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Q: -X Find the area bounded by : f(x)=e*, g(x) = ex and x=3.

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)=x²+2x+…

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

Q: In the indefinite Integral Sin(cosh x + ex)- integrand? A In(cosh x + ex) B sinh x + ex In(cosh x +…

A: The given function whose integral is to be found is called the integrand.

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

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Q: Solve the integral: A 6√√x +C B + C C D 37 6 3√√√x² √√√3/X 1x|m √x + C dx

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Q: Find the volume of solid generated by revolving the region bounded by f(x)= x² + 1and…

A: Volume

Q: If f(x) = A B tanx 1+e 1+1² 1+e¹ In (secx) √ 1+tan²x 1+ e tanx sec 3x tanx -dt, then f'(x) equals

A: solution:-f(x)=∫0tanx1+t21+etdtApplying leibniz integral…

Q: If g (x): A d dx [e' — In(2t+1)]dt, find g''(x) - -2 4 (2x + 1)² 4 B (2x+1)² Ⓒe*-In(2x+1) 2 D (2x +…

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

A: the point of intersection of  y=x-1 and y=(x-1)3  and y=0 are (0,-1),(1,0) and (2,1) the line…

Q: (A) B (C) (D) **/2 18 [*/ ces **/2 cos²0d0 18 sin²0d0 cos²0d0 0 of the 0 **/2 $ cos²0d0

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Q: f f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

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Q: y = x²sin (3x)

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Q: Determine the integral: x²cosxdx x²sinx + 2xcosx-2sinx + C B x²sinx-2xcosx-2sinx + C с…

A: Here we have to determine the given integral.

Q: S Given dx, determine all value/values of P for which the improper inte хр A (-∞,1] B {0,1} C…

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Q: Determine the integral: [x²cosxdx A x²sinx + 2xcosx+2sinx + C B x²sinx + 2xcosx-2sinx + C (C)…

A: Given,∫ x2cosxdx

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

A: We have to find derivative

Q: Using shell method, find the volume of R, when it is bounded by y = x³, x = 0, y = 8 about x- axis.

A: Shell method

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

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

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Q: =√x, x=4 and the x-axis, the limits of integration are: If a horizontal element is used to find the…

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Q: Given the integral sec6 (x - 1) tan4 (x - 1)dx, which of the following equatio useful for…

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