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

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: In the indefinite Integral in(cosh x + e*)- integrand? A sinh x + ex B In(cosh x + e*) In(cosh x +…

A: What is the integrand

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

A: The integration are

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: Question 33 Evaluate: :S₁ A B с D dx (x+1) log(x+1) -In[log(x+1)] +C In 10 -log² (x + 1) + C 2 -In…

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Q: y=Arccos (x²)

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Q: X lim x→1 x-1 Your answer x In x

A: Let's evaluate given function by using l'hospital's rule.

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 =…

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

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

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

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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: If g (x) = — _ _[e¹ — ln(2t+1)]dt, find g''(x) dx -2 (A) B C) D 4 et + (2x + 1)2 4 et + (2x+1)2 e* -…

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

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

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Q: Question 13 3 2 Evaluate the triple integral: f(x+y+z)dydxdz A) 24 B) 18 C) 6 D) 12

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Q: The gradient at any point (x, y) of a curve is given by dy-3x² +ax-36 where a is a constant. The…

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

A: To solve the integral.

Q: If f (x) = A) B (C) D tanx √1+1² 1+e' 0 1+tan²x tanx 1+e sec ³x -dt, then f'(x) equals tanx 1 + e In…

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Q: 5. (D²+4)y=4 cot 2x

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

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

A: B option is correct.

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

A: To find integrand the steps are as follows.

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: If y = arcsin (e5e), Check Answer dy da

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

A: According to the properties of definite integral(A) ∫abkf(x)dx=k∫abf(x)dx      True(B)∫abkdx=k…

Q: Evaluate the improper integral A) diverges 3 B 4 с N|9 2 3 -dx

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Q: y = 5 tan x³ + sec(3x)

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Q: 1 S dx 3 x + x Solve the integral: 5 A + x +C 1+x+c n 1+x+c in 1 B + x + C © 6/5+x²³/+c C ® 1+x+c In…

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

A: solution

Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx (3e)3+cosh2x A +C 2 + 2ln3 (3e)3+cosh2x 2ln3…

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

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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: 1. ²₂(x² − 2xy² + y²³) dx dy

A: Solve the following integration .

Q: y= 3 Arcsec 3x

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Q: A solution of a differential equation free from arbitrary constants obtained from the general…

A: The complete Solution of an Ordinary differential equation is composed of a general solution and a…

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

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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: We need to find volume.

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

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Q: Evaluate the improper integral 3 A 4 B) diverges с 0 D 2 N|O √√² 3³/3 m|f dx

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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: Solve the integral: A B с 1 √√x+x √√ Sin/1+x²|+c -In +C 6in|5+ x²|+C с {in/1+x³ |+c C dx

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

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

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