B S₁ Evaluate: A In 10 (В) ® -log² (x+1)+C 2 In 10 In[log(x+1)] + C -In 10 log2 (x+1)+C 2 D dx (x+1) log(x+1) -In[log(x+1)] +C

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: Question 14 If [ _ ( x + 1) dx S A B C D (x+2)(x-1)² 2 . 93 -io 1 6.11 1 -- - 9 9 2 - - 3 - 3 2 - 3…

A: To find the value of A and C  in the given integral.

Q: Solve the integral: A 5n/1+x²|+C 5 (B) 6in 5+x' 6In|5+ +C 음 m/1+x²|+c C ³√|+C 1+x √√√√x+x² dx D

A:

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

A:

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

A:

Q: Determine the area bounded by f(x)=x²-x and x-axis. unit² B unit² Ⓒunt² D unit²

A:

Q: How many A infinitely many B may vary depending on n none antiderivatives does a function of the…

A: Following the guidelines, please submit the second question again for its solution.

Q: 15 S A B (c) D (x+1)dx (x+2)(x-1)² 1 2 -- 9 1 2 " 9 3 -lo 1 9 " - - W|N 2 1 9 3 W|N 3 -S[₂ = A B +…

A:

Q: Find the area bounded by : f(x)=e*. g(x)=e" and x=3. (e²-1)2 A sq. units (e²+ 1)² e² -sq. units (e³+…

A: Now,The graph of the area bounded by f(x)=ex, g(x)=e-x and x=3 is shown below:

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: Evaluate the integral: 2 sin(3x)cos(3x)dx A B 1 4/6 —— 1 wlr 3 1 - wlw

A:

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

A:

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

A:

Q: Question 7 Evaluate: A B с dx (x+1) log(x+1) In 10 In [log(x+1)] + C 1 -In[log(x+1)] +C In 10 -log²…

A:

Q: The improper integral A e B 0 C D) 1 + ∞ [** 0 e-x dx is

A: The given improper integral is: I=∫0+∞e-xdx

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

A:

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

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: Question 10 Let f(x)=√3x-2 on the interval volume of the resulting solid. 43x 135 83m 125 83x 135…

A:

Q: Evaluate the triple integral: A) 6 B) 18 C) 24 D) 12 3 2 1 ²³√ [²√ √ 0 (x+y+z)dydxdz

A:

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…

A:

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…

A:

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

A: we have to find the integral by general power formula

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

A:

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

A: We can solve this as follows:

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

A: Here we have to determine the given integral.

Q: How many antiderivatives does a function of the form f(x)=x" have when n*0? A) none B) 1 infinitely…

A:

Q: Evaluate the triple integral: A) 12 B) 6 C) 24 D) 18 3 2 1 (x+y+z)dydxdz

A: We have to choose correct option

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

A:

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

A:

Q: (x + 1) dx A (x + 2) (x− 1)² = √ [ +42 + 15 S B + x-1 C (x-1)² dx, the values of A & C respectively…

A: answer is in next step . please give a like !!!

Q: If (x+1) dx (x+2)(x-1)² 1 93 2 93 S- A B D -io 1 W|N -io 2|3 2|3 9 3 A x+2 + B + x-1 C (x-1)² (x -…

A:

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: Question 20 Determine the area bounded by the functions f(x) = (x + 1)³ and A unit² А 3 Ⓒunt² B 3 C…

A:

Q: Determine the area bounded by f(x)=x²-x and x-axis. (A) 4 -unit² B unit² -unit² -unit² Ⓒ 1 15 2

A:

Q: Evaluate the improper integral 3 A 4 B) diverges C D —— 6/0 m|+ ² 0

A: Topic:- application of integration

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: y = 2 sin 3x 1+3cos2x

A: We can solve this as follows:

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

A:

Q: Given A) B (C) D 11 √ √ ² f(x) dx = = /10 f(x) dx = 0 and 11 6 20 55 •[ 37/(x)dx - 5² 2/(x)dx…

A: D option is correct.

Q: dx using miscellaneous substitution will yield to secx + 1 nsforming - S 1+2 / dz √²-22² dz 1+z²…

A:

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

A: To evaluate the integral. Option A is correct.

Q: Evaluating √√9-x² dx using trigonometric substitution will lead to: 57/2 A 18 "/2 cos²0d0 35*1/2 B…

A: ANS: B

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

A:

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

A:

Q: If f (x) = A (В B C D Stams. 0 sec²x tanx 1+1² Ite¹ 1+e tanx sec ³x 1+e -dt, then f'(x) equals tanx…

A:

Q: dx Evaluate the integral: (+3x-7) A ++ In|3x-6|+C 5 +5x+! In/x-21 +C B 3 с +5x+31n|x-2|+C D x² + 5x…

A: You must have idea about logarithmic properties to simplify this expression. Understanding of…

Q: Which of the following can be determined given 3 A - (f(x) = g(x))dx B (4f(x) +9h(x))dx 3 © (f(x) +…

A: g(x) is integrated in the interval 0 to 3 f(x) and h(x) are integrated in the interval 0 to 3