Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx 3+ (3e)3 + cosh2x A + C 2+2ln3 (3e)3 + sinh2x (B) 2ln3 (3e)3 + cosh2x (C) 2ln3 (3e)3+ sinh2x D 2 + In3 + C - + C + C

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

A: Option (B) is the correct answer.

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

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: If 8(x) = [e²-m (21+ - dx S[e²-In (21+1) ]dt, find g(x). -2 A e-In(2x+1) 4 B (2x + 1)² 2 Ⓒ (2x + 1)²…

A:

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

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Q: 15+0. The improper integral e* dx is

A:

Q: Question 5 -S_(x + 1) dx A B (x + 2) (x - 1)² = √ [1+2+ = ²1+ x-1 If B -ia 9 9 W|N 1 9 3 1 9 3 دا |…

A: find out the value of A,B and C

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 1 [₁f(x) dx = 0 and -1 1 S²F(x f(x) dx = 11 6 I evaluate 1 √²3f 3f(x) dx - .0 -1 2f(x) dx.

A: Explained below

Q: Question 36 Evaluate the triple integral: (x+y+z)dydxdz 0 A 24 B) 18 (C) 6 D) 12

A:

Q: Solve the integral: A 6√√x +C B + C C D 37 6 3√√√x² √√√3/X 1x|m √x + C dx

A:

Q: (x2y3 - 1+) dx + x3y2dy = 0 1+9x2

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: y = 3t 1+t³ X= 3t 31² 1+t²³

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: Stan² √I+1² 0 l+e' 1+tan²x tanx 1+e In (secx)√1+tan²x 1+et tanx sec²x 1+elanx sec 3x If f(x) = A B…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Let f(x)=√3x-2 on the interval volume of the resulting solid. W|N - Revolve the region between the…

A:

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

A: Solved below.

Q: B $S₁ (x+2)(x-1)² = √[=42+²1+ (-₁2). (x 1)² ]dx, 1 x-1 A B C If -io 9 -ja -ia 2/3 1 2|3 2/3 2 the…

A:

Q: 1 1 11 f_²_f(x) dx = f(x) dx = 0 and f(x)dx [² f(x) dx = 1 1 ₁ 6' 1 0 [²3F(x) dx - √ 2P(x)dx -1 11 6…

A:

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. A (e²-1)² e2 sq. units (e²+ 1)² e2 (e³-1)²…

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: Which of the following is NOT a method for finding volume of solids of revolution?

A: answer is in next step

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

A: A detailed solution is given below.

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

A: A detailed solution is given below.

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

A:

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

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: Given the integral sec6 (x − 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: The given integral,       ∫sec6x-1tan4x-1dx

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1

A:

Q: Find the volume of the solid generated using washer method by revolving the region bounded b y = x²…

A: Let's find volume of solid by using washer method.

Q: Solve the integral: A 3√√x² B + C 6 C 6√√x + C с D 3³√√x² +C ကြ Sv √√√x 3√x X dx

A:

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

A:

Q: 11 |_₁_f(x) dx = 0 and ² f(x)dx==1₁ 11 5 Given A Ⓡ 555 B 6 C D 킁킁 11 6 0 evaluate [²3f(x) dx -…

A: B option is correct.

Q: Question 27 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct…

A: A detailed solution is given below.

Q: To evaluate the integral si sin³0cc 1³0cos 60d0 by trigonometric transformation, we use the identity…

A:

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

A: Given problem:-

Q: 1 X + X Solve the integral: Gin|5+x²|+C A 5 @ B {/in/1+x³²|+c C © =√³ m/₁ + x ²³ / + C 6 ©…

A:

Q: Which of the following can be determined given f(x) dx = 5₁ x) dx = 5,₁ ₁ g(x)dx=7, and h(x) dx = -5

A:

Q: Evaluate the double integral: A 40 B 80 C 60 30 ²(3x² +9y²) dxdy

A:

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

A:

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

A:

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

A: To solve the integral.

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

A: Integration

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

A: Definite integral Property : ∫ab fx±gx dx = ∫ab f(x) dx ± ∫ab g(x) dx. ∫ab k f(x)dx =k∫abf(x)dx ;…