Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)=x²+2x+ 5about the x-axis. A 72 unit ³ (B) 63 unit ³ 56x unit ³ 37x unit ³ D

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

A:

Q: tretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: Topic:- calculus

Q: Question 27 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct…

A: A detailed solution is given below.

Q: Which of the following can be determined given f(x) dx = 5, g(x) dx = 7, and Sh(x) dx = -5 3 A √…

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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 +…

A:

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: Given the integral sec (x - 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: Let's find useful formula for evaluation of integration.

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

A:

Q: Given 1 [₁f(x) dx = 0 and -1 1 S²F(x f(x) dx = 11 6 I evaluate 1 √²3f 3f(x) dx - .0 -1 2f(x) dx.

A: Explained below

Q: Which of these expressions represents the area bounded by y = 1/2 x^2 and y = 3x? * 6x + x²dx 6x…

A: To solve the following problem

Q: Question 14 dx Transforming - using miscellaneous substitution will yield to secx + 1 1-z² A 1+z²…

A: Here we have to transform the given integral by using miscellaneous substitution.

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

A:

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

A: Here is the solution of the given problem. We solve this by using shell method

Q: 4 Evaluate the double integral: 2ydydx 1 A B (ⒸⒸC) D m 100 8 +10 9 2 5 2

A: On solving this we will get  Option (C) is correct

Q: Evaluate the double integral: A B C D m 100 +10 9|N NIG 4 S** 2ydydx 1

A: A detailed solution is given below.

Q: An engineer is designing the runway for an airport. Of the planes that will use the airport, the…

A: Given:   To determine: The minimum allowed length for the runway.

Q: q13

A: We have to calculate the given indefinite integral

Q: Given √√2/10 dx, determine all value/values of P for which the improp хр onverges? A) {0,1} B)…

A: Topic:- application of integration

Q: 17. Evaluate [9e³x dx O9e³c+1 3c+1 O9e3c O9ec-3 3e³c-3

A:

Q: Find the volume of R using shell method, when R is bounded by y = √x - 2, y = 0 and x = 4 about the…

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

A: We know eln(x) =x

Q: Solve

A: We have to calculate the given indefinite integral

Q: To evaluate the integral sin³0cos0de by trigonometric transformation, we use the identity; A sin²0=…

A:

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

A:

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

A: Determine the area bounded by the function f(x)= (x+1)3, g(x)= x+1 .

Q: (x2y3 - 1+) dx + x3y2dy = 0 1+9x2

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

Q: X+2 Determine the case of the following proper rational function after simplification: (x² – 4)(x³ –…

A:

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: 1 Solve the integral: S dx 3 x ที่ X + X h_1+x+c A C Ⓡ 6ın|5+x=³² | +C B © h1+x8 l+c + C h1+x+c D +…

A: Given that we need to solve the following  integral.

Q: In the indefinite Integral Sin(cosh x + ex). integrand? sinh x + ex cosh x + ex dx, what is the

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Q: Evaluate the improper integral A diverges B) 0 с 3 Alu 112²232/3 dx 4

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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…

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Q: What kind of polar graph has the equation r = 3 ? * cardioid lemniscate circle rose petal

A: Solution: equation r=3

Q: e the integral: S- 1 √x © $ n/²+x²³/+c +C © ²0/₁+x²³²/+c\ +C == n/₂+x²³/+c +C √x+x dx

A:

Q: ion 8 apply General Power Formula of Integration on which of the following sinhucothudu cosha coshu…

A: We have to choose the correct option from the given options

Q: Given S dx, determine all value/values of for which the improper integral XP converges? (A) {0,1} B…

A: Please follow the next step.

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

A:

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

A: To find the area bounded by curves

Q: Question 11 Let g be a differentiable function, and let the range of g be an interval 1. Suppose…

A: The integration are...

Q: Determine the case of the following proper rational function after simplification: X+2 (x²-4)(x³-8)…

A: Correct option is missing

Q: Question 37 1 Solve the integral: S- dx √√√√x+x A m/1+ + X +C ℗ 6n/5+x²³| +C B Ⓒ1+x²+c с X C =…

A:

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: A detailed solution is given below

Q: Evaluate the double integral: 2ydydx A 4 9 B) m 100 8 NIG 2 9 2

A: To find the value of given double integral.

Q: Question 31 Evaluate the integral: A B C D H|m 1 1 13 1|6 sin(3x)cos(3x) dx

A: To evaluate the integral.

Q: Evaluate the improper integral (A) diverges B (Q) Na O ساح 3 1²23 -dx

A:

Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A:

Q: Question 16 d If g(x) = == S[e²-In (21+1) ]dt, find g(x). dx 4 A et + (2x+1)2 e* -In(2x+1) 4 e¹+ (2x…

A: We will first find g(x).

Q: If ƒf (x) =¸ (A) (B) Sº sec²x 1+elanx In (secx) √✓ 1+tan²x tanx 1+e sec ³x tanx 1+e 1+1² tanx…

A: Using Leibnitz integral rule.

Q: Question 10 If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis,…

A: Horizontal element

Q: Question 12 We can apply General Power Formula of Integration on which of the following integrals? A…

A: