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

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A: To find the area bounded by curves

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

A: consider9x2+6x-7=9x2+6x+9-16=9(x+3)2-16 let u=x+3⇒du=dxThen9(x+3)2-16=9u2-16

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

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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…

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Q: Evaluating √9-x² dx using trigonometric substitution will lead to: **/2 Ⓒ 18/¹/2 (A) sin²0d0 0 **/2…

A: See the details solution in below

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A: Let's find integration of given function.

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A: The volume of the solid is 63π unit3

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

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Q: wen 1₁² / 0x хо A) (-∞0,00) B (1,00) C{0,1} D) (-∞,1] -dx, determine all value/values of P for which…

A: Here  , we have two cases when p=1 and when p not equal to 1.

Q: - States √1+1² * tanx V1+t2 0 1+e' 1+tan²x 1+ e tanx In (secx) √ 1+tan²x 1+ e tanx If f (x) = A B…

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

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Q: πT Evaluate the integral: S sin(3x)cos(3x) dx

A: We can solve this as follows:

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

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Q: The improper integral (A) e B) 0 с 00 D 1 8 0 edx

A: ∫0∞e-xdxSubstitute u=-x→dudx=-1→du=-dx=∫-e-x

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

A: Here we have to find the integral for finding the volume.

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

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

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A: Let's find useful formula for evaluation of integration.

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A: To solve the integration using properties and given data.

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

A: Topic:- application of integration

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: Evaluate

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Q: 1 11 Given 1 [²_f(x) dx = 0 and [ f(x) dx = 1 1 ₁ ¹3f(x) dx - 2f(x)dx. evaluate 6 0 -1 55 A 6 11 B 5…

A: A detailed solution is given below.

Q: iven ·S. A (-∞0,00) B) {0,1} Ⓒ(1,00) D) (-∞,1] dx, determine all value/values of P for which the…

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Q: Given [₁₂f(x) dx = 0 and A 0 B Ⓒ D √ √ ² f(x) dx = ²1 55 11 11 5 11 6 " •√²3f(x) dx - √₁2f(x) dx.…

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

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Q: How many antiderivatives does a function of the form f(x) = x^ have when n=0? A may vary depending…

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Q: Question 5 3 Evaluating √9-x² dx using trigonometric substitution will lead to: A 35*1/2 cos²0d0…

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Q: Which expression is equivalent to O cotx+sec x O cos x + cot a Otan x+sec x O sinx+tan x an £ ? cos…

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Q: Evaluate the integral: Se3+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 - + C (3e)3 + cosh2x B…

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Q: Can you please write out on paper how to solve this equation? I can't understand the typed out…

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

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Q: Transforming S Ⓒ / ² A 1-z² 1+z² ® / 12-2 B 1+z² © Ⓒ S ²¹²+² dz 1-z2 1+z² D S 1-z² dx secx + 1 -dz -…

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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.

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A: Given that g(x) is a differentiable function and range of g(x) is interval I. f(x) is a function…

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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…

A: According to the properties of definite integral(A) ∫abkf(x)dx=k∫abf(x)dx      True(B)∫abkdx=k…

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

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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: In the indefinite Integral Sin(cosh x + ex). integrand? sinh x + ex cosh x + ex dx, what is the

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

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