Question 32 dx Evaluate: (x+1) log(x+1) A) -In 10 log2 (x+1) + C 2 B --log² (x+1)+C 2 In 10 In[log(x+1)] + C ____In[log(x+1)]+C In 10 D

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

A: We will evaluate the given integral using simple Integration rules.

Q: How many antiderivatives does a function of the form f(x)=x" have when n*0= A) infinitely many (B)…

A: We have to choose option find antiderivative

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

A: On solving this we will get

Q: If f(x) = A B D tanx S™ 0 1+tan²x 1+etanx sec ³x l+etanx In (secx)√1+tan²x 1+etanx sec²x tanx 1+12…

A: Using the Leibnitz rule:

Q: To evaluate the integral sin³0cosº0de by trigonometric transformation, we use the identity; 1- cos20…

A:

Q: Question 33 If g(x)=- A) B D d = 2√²-1 (2 ·S^*^[e'-In(21+1)]dt, find g''(x) - 4 (2x+ (2x + 1)² e*…

A: Solved below.

Q: e integral: J √√√x+x F1+x X + C 1 x C 5 + C 6in|5+ x² +C 6

A:

Q: Determine the integral: [x²cosxdx

A:

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

A: Always false

Q: A bullet is fired with muzzle velocity of 150 m/s at an angle of elevation = 45°. Gravity = 9.8…

A: Since you have posted a question having multiple sub part as per guidelines we can solve only first…

Q: etermine the area bounded by f(x)=x²-x and x-axis. 1 A unit² 2 B unit² 1 unit² 1 unit² D

A:

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: tank has pure water flowing into It at 10 L/ min. The contents of the tank are kept thoroughly…

A:

Q: Question 9 Which of the following represents the volume of the solid generated by revolving the…

A:

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

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: Integration

Q: dx A B C S (x+2)(x-1)² = √ [+4+2+ = -1 + (-1) 2 ]dt @ - - - - 13/12 A 9 If dx, the values of A & C…

A:

Q: Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 + C (3e)3+cosh2x B 2ln3…

A:

Q: Evaluate the integral: e3+cosh2x33+cosh2xsinh2x dx (Α) (3e)3+ sinh2x 2+In3 + C (3e)3+cosh2x B 2+2ln3…

A:

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

A:

Q: 25

A:

Q: If (x+1) dx (x+2)(x-1)² S -=S= A B + x + 2 + x-1 C (x-1)2 dx, the values of A & C respectively are:

A:

Q: To evaluate the integral sin³0cos ede by trigonometric transformation, we use the identity; A sine…

A: On solving this we will get  To evaluate the given integral we use the the identity in given option…

Q: The improper integral (A) e B) © ⒸO D 1 8 Stoe ex dx is

A: Given that,

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

A:

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

A: D is correct option.

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

A: We have to choose correct option

Q: B C) + et. + 4 (2x + 1)² 4 (2x + 1)²

A:

Q: (x+1)x (x+2)(x-1)² If f @ 1/1 1/1/0 93 B C D 9 . - 2 3 2 9 3 - 2/3 . 93 A B 421 + + x+2 C (5-131].…

A: Explained below

Q: y = x²sin (3x)

A:

Q: d^3-5d+4)y=0 when, x=0, y=-2, dy=9, d^2y=0

A:

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: solve the following differential eqaution : (2x+y)dx-(4x+2y-1)dy=0

A: Solved below.

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

A: Substitute sec^2u=1+tan^2u B option is correct.

Q: 1 √√√√√x + x S Solve the integral: 5 @ =³√√/1+ x ³²³/ + C A {m/1+x²³² |+c ==ınlı 5 6 B C ©…

A:

Q: + 1) dx A B C (x + 2) (x - 1)² = √ [++^2 + == 1 + (0-12 dc. ]dx. dx, the values of A & C…

A:

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: dx (x+1) log(x+ ) In[log(x+1)] + og² (x+1) + C

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

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

A:

Q: Evaluate the integral: Sen(1²2+3x-7) е dx A x² + 5x+In 3x-6|+C XZ B +5x+31n|x-2|+C 2 C x ²2+ = +…

A: On solving this we will get

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…

A:

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

A:

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

A:

Q: 2x ind the derivative of: 2e cos(8x). [Hint: use product rule and chain rule!] se e^x for e*. ow,…

A:

Q: What kind of the polar graph has the equation r = 2 + 2 cos 0? limacon cardioid lemniscate…

A:

Q: S Given 1 хр for which the improper integral converges? A {0,1} (B (1,00) C (-∞0,00) D (-∞,1] dx,…

A: The given improper integral is: ∫1∞1xpdx Suppose p=1 then: ∫1∞1xdx=ln x1∞=∞ So, diverges.

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