d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4 (D) (2x + 1)² et +

Q: Evaluate the integral: A 16 밴 3 sin(3x)cos(3x)dx

A: ∫sin(3x)cos(3x)Substitute u=sin(3x)→dudx=3cos(3x)→dx=13cos(3x)du=13∫uduWe know that…

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

A:

Q: Please write out/show work, thank you! Find the slope of the line tangent to 2xy + π sin y = 2π…

A:

Q: Question 5 The improper integral A e B) 0 (C) D 1 8 +∞0 Se ex dx is

A:

Q: A lighthouse is on an island 400 meters off shore. The lighthouse beam makes a full turn every 15…

A: answer is in next step

Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

A:

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

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: 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: dx using miscellaneous substitution will yield to secx + 1 Transforming S Ⓒ √ ²² +²2 dz (Α) -z²…

A: This question can be solved by substituting z=tanx2

Q: Evaluate the double integral: S²² (3x² +9y²) dxdy 0

A:

Q: Question 12 Given S (A) (-∞0,00) B (1,00) D -dx, determine all value/values of P for which the…

A: Here we have to determine all values of p of the given improper integral in which the integral is…

Q: Question 15 Evaluate the double integral: (A) 40 B) 80 C) 60 (D) 30 ²² 6) (3x² +9y²) dxdy

A: we can find the double integral.

Q: Evaluate the integral: Se³+ cosh2x33+ cosh2xsinh2x dx 3+ (3e)3 + cosh2x A + C 2+2ln3 (3e)3 + sinh2x…

A:

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: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 A 355/20 cos²0de 0 **/2 B Ⓒ 18…

A: Evaluate using trigonometric substitution ∫-339-x2dx=?

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

A:

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

A: In this question, we want to know that on which of the following integrals we can apply the general…

Q: Question 19 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct…

A:

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

A:

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

A: To find the area bounded by curves

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: We will have to find  qrea bounded by rhe curve  y= x1/2  X=4 and xaixs

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: If f(x) = (A) B C D tanx sec ³x 1+e 1+1² 0 sec²x 1+ e tanx In (secx)√√ 1+tan²x tanx 1+e 1+tan²x 1+ e…

A:

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

A:

Q: ral: Seln(2x²+3x-4)³ (4x+3)dx

A:

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

A:

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

A:

Q: Question 14 dx Transforming - using miscellaneous substitution will yield to secx + 1 1-z² A 1+z²…

A: Here we have to transform the given integral by using miscellaneous substitution.

Q: 1 3√x + x X Solve the integral: J 6 5 F1+x8 + c A @ c in 1 B 1+x + C © n1+x.c C C Gin|5+x²|+C D - dx

A: Explained below

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: Question 20 How many antiderivatives does a function of the form f(x)=x" have when n*0₂ (A) 1 (B)…

A: Antiderivative means Integration

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

A:

Q: Evaluate the double integral: A B C D m|m NIG 2 2ydydx

A: You must have an idea of double integration to solve this problem. Option D is the right choice. The…

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

A:

Q: Evaluate the double integral: A B D) 9|N 2 N|G m 100 3 8 •√x 1. √ √V 24 +10 2ydydx

A: Evaluating the double integral

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

A:

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

A: Conic method

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

A:

Q: feschucoshudu cschusinhudu sinhucothudu cosh coshu sinhudu O fir

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: 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: Consider the vector field. F(x, y, z) = (9ex sin(y), 2e sin(z), 4e² sin(x)) (a) Find the curl of the…

A:

Q: Question 1 Solve the integral: Seln(2x²+3x-4)³ (4x+3)dx A eln(2x²+3x-4) (4x+3) 3(2x²+3x-4)…

A: To evaluate the given indefinite integral.

Q: Let f(x)=√3x-2 on the interval. 1] Revolve the region between the curve, y=1 and y-axis about the…

A: Here is the solution of the given problem. We solve this by using shell method

Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

A:

Q: Given A B с D f(x) dx = 0 and [ f(x) dx = 11₁ -1 11 6 55 6 0 11 5 - S²3f(x) dx - √₁2 f(x) dx.…

A:

Q: Which of the following can be determined given 3 3 [ f(x)dx=5₁ g(x)dx=7, and √ √h(x) dx = -5 3 A √…

A: See the details solution in below

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

A: