To evaluate the integral sin ³0cos (A) sin²0=1-cos²0 1-cos20 B sin ²0 2 sin20 sin cose 2 1+ cos20 cos²0= 2 D sin ³0cos Ode by trigonometric transformation, we use the identity:

Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

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Q: If the Laplace transform of f(t) = e cos(et) + t sin(t) is determined the a. a shifting theorem can…

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

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

A: We can solve this as follows:

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…

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Q: sinh xte cosh x + ndefinite Integral Sin(cosh x + e*)- In(cosh x + e*) sinh x te cosh x + ex

A: We have to calculate the given indefinite integral according to the given information

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Q: Evaluate the triple integral: 3 2 1 S³ S² S²(x+y+z)dydxdz 0 A 12 B 18 C 6 D) 24

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

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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: 2+3x-4) (4x+3) dx Solve the integral: eln(2x²+

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

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Q: Let f(x)=√3x-2 on the interval axis and find the volume of the resulting solid. 43л -unit 3 135 83…

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Q: The improper integral A) 0 B 1 C D) e 8 ·+∞o Ste ex dx is

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Q: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: We have to find out derivative

Q: dx S secx + 1 1+z² Ⓒ √ 1+ 2²/ dz S A 1-z² -z² B 1+z² © √²/²+²/d² S³ -dz 1-z² 2-2z² / 1²= D 1+z²…

A: Note: According to our expert guidelines only first individual question is to be answered kindly…

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

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Q: Which of the following can be determined O [ars) A (4f(x) + 9h(x) dx B [²³(f(x) + g(x) (f(x) + g(x)…

A: We have to find out

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

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

A: Find:when we can use power formula

Q: S Given dx, determine all value/values of P for which the improper inte хр A (-∞,1] B {0,1} C…

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Q: y = Arctan (2x)

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Q: y=Arccos (x²)

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

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Q: 25

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

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Q: -Je cosx dx

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Q: + ∞o [** S The improper integral A B) 1 8 ex dx is

A: ∫0∞e-xdxSubstitute u=-x→dudx=-1→dx=-du=-∫euduWe know that ∫audu=auln(a)

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

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

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

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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: Find the volume of R using shell method, when R is bounded by y = √x - 2, y = 0 and x = 4 about the…

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

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: find out the work required fo stretch the spring an additional 3 ft.

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 ;…

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 1 A -unit² (B) unit² 1 H|m

A: Given that fx=x+13  and gx=x+1Solution :x+13=x+1x+13-x+1=0x+1x+12-1=0x+1=0 and x+12-1=0x=-1 and…

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

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Q: Question 12 We can apply General Power Formula of Integration on which of the following integrals? A…

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

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Q: I the area bounded by : f(x)=e*, g(x) = ex and x=3. -X ) (e²-1)² sq. units e2 (e³ + 1)² e3 (e³-1)²…

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Q: Find the area of shaded region. 1/4 sq. unit 1/2 sq. unit T/4 sq. units 1/2 sq. units j r² = sin 20

A: The shaded region is bounded by the polar curve r2=sin2θ in the first quadrant.

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

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

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

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Q: Q/IF 3 = sin(x) 0²³²141 y= (4) y = 3/2 I sin(x) cos(x) Prove that

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

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