If f(x) = A B C D tanx S 0 sec²x √1+1² 1+e¹ -dt, then f'(x) equals 1+e tanx In (secx)√1+tan²x 1+ e tanx sec ³x 1+etanx 1+tan²x tanx 1+e

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: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 [*1/2 cos²0de A 0 Ⓡ IS!" B 18…

A:

Q: dx secx + 1 Transforming S Ⓒ 1 +²2² A 1-z² (В) / z²+z 1-z² 2-2z² © 1+z² -z² Ⓒ S 1=32/2/dz D 1+z² -dz…

A: Solve using miscellaneous substitution

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

A: Let's find volume of two curves rotating about x axis.

Q: w/N Let f(x)=√√3x-2 on the interval y-axis and find the volume of the resulting solid. Revolve the…

A: Application of integration

Q: Determine the area bounded by f(x)=x²-x and x-axis. 2 A unitz Ⓡunit² unit2 1 D 4 -unit²

A: We will integrate the f(x) between limits 0 to 1.

Q: e: Sz dx (x+1) log(x+1)

A:

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

A:

Q: f(x)=√3x-2 on the interval Let of the resulting solid. 83 (A) -unit 3 135 43x B -unit3 125 83x…

A: Ans : A

Q: Evaluate the integral: A B C D H|m 1 6 1 |ო 3 √ sin S 1 6 sin(3x)cos(3x) dx

A:

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: πT Evaluate the integral: sin(3x)cos(3x) dx រ 1 A 3 (B) i D 1 براس 1

A:

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: Let the integral be 'solvable' using trigonometric substitution. What is the 9 choice of u given J…

A:

Q: dx Evaluate: s (x+1) log(x+1) A --In 10 log² (x+1)+C 2 B In10 In[log(x+1)] + C с = -log² (x + 1) + C…

A:

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

A: The region bounded by line y = x - 1 and the curve y = (x - 1)3 is as below

Q: Determine the area bounded by f(x) = x² − × a axis. A - unit² B unit² C unit² 2 -unit? +|5

A:

Q: Solve the integral: Seln(2x²+3x-4)²³ (4x + 3) dx (2x²+3x+4)4 (A) + C 4 B eln(2x²+3x-4)³ (4x+3)…

A: To solve the integral.

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

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 gi…

A: To solve the integral.

Q: dx (x+1) log(x+1) 1 In[log(x+1)]+C In 10 -In 10 log² (x + 1) + C 2 In 10 In[log(x+1)] + C -aluate: A…

A: Topic:- application of integration

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

A:

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

A: We have to find out simplification

Q: Question 23 en [ "_f(x)dx=0 and ["f(x)dx = 1, evaluate Given A 0 B (u) D 11 76 55 =¹3f(x) dx -…

A: We have to find out the 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: Given problem:- If a horizontal element is used to find the area bounded by y=√x, x=4 and the…

Q: cos²u= 1+ cos2u 2

A:

Q: X-2 Se Evaluate the integral: (+3x-7) dx A x²+5x+In 3x-6|+C B +In|3x-6|+C C + In/x-21 +C 3 D)…

A: Solution:

Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

A:

Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, th (A) 0 and…

A: Topic:- application of integration

Q: d If g (x) =-=-^[e'- In(2t+1)]dt, find g''(x) . dx -2 A ex-In(2x+1) 4 B et + (2x + 1)2 4 (2x+1)2² 2…

A:

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 C=/2 A 18 cos²0d0 (B) 1852/200…

A: See the details solution in below

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

A: solution

Q: y 3 Arcsec 3x

A: Find out the y'.

Q: d If g(x) = - S* [e'− ln(2t+1)]dt, find g''(x) dx -2 2 A ex. (2x + 1)² 4 (В B et + (2x + 1)² Ⓒe*…

A: Given that gx=ddx∫-2xet-ln2t+1dt

Q: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

A:

Q: Given √ 1 pdx.c A (-∞,1] B (1,00⁰) Ⓒ (-∞0,00) D (0,1) dx, determine all value/values of P for which…

A: This can be solved as follows:

Q: Evaluate the improper integral A 0 (B 4 C diverges 2 D 9 mit 2 3 -2 X 3 dx

A:

Q: y = x^Arctan *(x4)

A: We have to solve derivative

Q: luating√√9-x² dx using trigonometric substitution will lead to: **/2 sin²0d0 3 of th 9[*/ cos²0de…

A:

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: Evaluate the definite integral by substitution: 21 1 dx 3/(1+3r)² (1) ² 3/1 + 13xdx 10 (3) [TV. (3)…

A:

Q: 2+3x-7) X-2 dx Evaluate the integral: Se A²+ +In|3x-6|+C Ⓡ 1/²/₁ 2²+5x+! In/x-21 +C B 3 x²+5x+In…

A:

Q: Solve the integral: A B C D 6√√x +C 3√x² + C 6 33³√/ x² +C √√√x 37 ကြ 3√x dx

A:

Q: Evaluate the double integral: (3x2² +9y²) dxdy (A) 80 B) 40 Ⓒ30 (D) 60

A: To evaluate the double integral: ∫02∫0y3x2+9y2dx dy

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

A: Solved below.

Q: Solve the integral: Seln(2x²+3x-4)³ (4x+3) dx (2x²+3x+4)¹4(4) A + C 3 eln(2x²+3x-4)³ B + C…

A:

Q: . The daily amount of smog produced by cars coming into a city is given by y = 2 + 0.01x3/2, where y…

A:

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

A: