Determine the area bounded by f(x)=x²-x and x-axis. 1 (A) -unit² B -unit² © == unit² C Ⓒ / / unit² D ~/3 16 H|4

Q: Transforming S Ⓒ / ² A 1-z² 1+z² ® / 12-2 B 1+z² © Ⓒ S ²¹²+² dz 1-z2 1+z² D S 1-z² dx secx + 1 -dz -…

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

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

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Q: y = x ¹ Arctan 4(x4)

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Q: Evaluating ³√9-x² dx using trigonometric substitution will lead to: 15/2 A cos²0d0 B 18 cos²0d0…

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Q: The improper integral A) 0 B 1 C D) e 8 ·+∞o Ste ex dx is

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

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x+1. 3 A unit² 3 Ⓒunt² unit² D…

A: topic- area bounded by curves

Q: s (x+1) log(x+1)

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Q: Determine the area bounded by f(x)=x²-x and x-axis. 2 A unit² ® —— unit ² 1 -unit² Ⓒ 1 -unit²

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Q: 3+cosh2x33+cosh2xsinh2x dx Evaluate the integral: e3+c (3e)3 + sinh2x A + C 2 + In3 (3e)3 + cosh2x B…

A: You must have idea of integration to solve it.

Q: X √√/31/22 Solve the integral: 3√/x² A + C 6 B 6√√√x + C C3√√√x² + C C) dx

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

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

A: find out the work required fo stretch the spring an additional 3 ft.

Q: (x+1) dx (x+2)(x-1)² 2 3 If 15 S. A B (C) D -10 2 . 9 3 W|N I 93 9 —— 3 =1[₂ = A x + + B x-1 +…

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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: 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: 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 sq. units…

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

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

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

A: A detailed solution is given below.

Q: -Je cosx dx

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0₂ (A) 1 (B) none may vary…

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Q: If g(x) = -S^*[e²− ln(2t+1)]dt, find g''(x) . dx 2 (A (2x + 1)2 Be* -In(2x+1) 4 (C) Ce¹+ (2x + 1)² 4…

A: Here is the solution of the given problem.  By using derives under Integral.

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: 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: cylinder cone pyramid if this triangle is rotated about the x axis, what figure is formed?

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Q: Question 5 The improper integral +∞0 5+0⁰ 0 ex dx is

A: We can solve this as follows:

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 3 A 2-unit² B -unit² с…

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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: sinh x + ex cosh x + ex In the indefinite Integral in(cosh x + ex)- dx, what is the integrand?

A: Intergrand

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: 3+ Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx (3e)3+ sinh2x A +C 2+In3 (3e)3 + cosh2x +C…

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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: Question 6 Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1, A unit² Ⓡ®…

A: Just plot the graph and see which is above and below to each other and find intersection point

Q: Q/IF 3= sin(X) (²314) y = 3² sin(x) cos(x) Prove that

A: To find y':

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: integral sin ³0cos Odt sin20 2 sin²0 = 1 - cos²0 1+ cos20 cos²0= 2 1- cos20 (D) sin²0= 2 To evaluate…

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Q: Evaluate the integral: Se³+ A B C 3+cosh2x33+cosh2x sinh2x dx (3e)3+cosh2x + C 2+2ln3 (3e)3+ sinh2x…

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Q: 14. Evaluate [4³x dx 3x O 4³x 3x +C 6ln2 O 4³x In4 O 43x+1 3x+1 +C O None of these +C

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Q: Find the volume of solid generated by revolving the region bounded by g(x)=x²+2x+ 5about the x-axis.…

A: Given:      fx=x2+1      gx=-x2+2x+5  Volume of solid revolving around the region is…

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

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Q: The improper integral A B if the 0 1 0 e dx is

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

A: the line y=x-1and y=(x-1)3 intersect in the points (0,-1),(1,0) and (2,1) the line y=x-1 is below…

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

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Q: Let f(x)=√√3x-2 axis about the y-axis and find the volume of the resulting solid. 43x A -unit 3 135…

A: Ans: C

Q: Find the volume of solid generated by revolving the region bounded by f(x)=x²+1and g(x)=x²+2x+5about…

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

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

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

A: In this question, we want to know the integrand of the given Integral.

Q: 46x Evaluate dx 2 Use rationalizing substitution. (A) none of the choices Be (ex - 2)1/² - √8 Arctan…

A: Let's find integration of given function.