Which of the following can be determined given 3 3 3 [ f(x) dx = 5₁ g(x)dx=7, and 1 [n(x) dx = -5 ₂3 (A) (f(x) + g(x) + h(x)) dx 3 B f (4f(x) +9h(x)) dx 4 Ⓒg(x) dx 4 3 Ⓒ [[F(x) - g(x)) dx

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 f(x)=x²-x and x-axis. (A) 4 -unit² B unit² -unit² -unit² Ⓒ 1 15 2

A:

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:

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: tanx If f(x) = (Α) B C D S 0 sec ³x 1+etanx In (secx) √ 1+tan²x tanx 1+e sec²x 1+ etanx 1+1² -dt,…

A: Here, given that: f(x)=∫0tan x1+t21+etdt...(1)

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

A: To find the area bounded by curves

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: Evaluate the double integral: A) 80 B) 30 C 60 D 40 √²² (3x² +9y²) dxdy 0 0

A:

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

A: B option is correct.

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

A:

Q: Find the volume of solid generated by revolving the region bounded by f(x)=x²+1and g(x)=x²+2x+5about…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: √ Given A B CO f(x) dx = 0 and 11 55 6 √ √²+ f(x) dx = 1/201₁ 11 6 , evaluate √3 3f(x) dx - ₁2 f(x)…

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

Q: the indefinite Integral In(cosh x + ex)- A In(cosh x +ex) Sinh x + e* cosh x + ex (В sinh xtex sinh…

A:

Q: Question 21 dx Evaluate: S (x+1) log(x+1) (A) In 10 log² (x + 1) + C 2 B In[log(x+1)] +C In 10 C…

A: We need to evaluate integral.

Q: Evaluate the double integral: 4 LA LE 2ydydx

A:

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

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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:

Q: If g(x) = d __*[e' - In(2t+1)]dt, find g''(x) . dx -2

A:

Q: The gradient at any point (x, y) of a curve is given by dy-3x² +ax-36 where a is a constant. The…

A:

Q: Which of the following can be determined given (A) L²³ F(x (f(x) + g(x) +h(x))dx g(x) dx © L² F…

A: We can solve this as follows:

Q: Determine the area bounded by f(x)=x²-x and x-axis. 2 A unit² ® —— unit ² 1 -unit² Ⓒ 1 -unit²

A:

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

A: Given, ∫ 9/√(x2+6x-7) dx We can calculate using substitute method

Q: x²+3x-7 X-2 +5x+31n|x-2|+C + +In|3x-6|+C 2 x²+5x+In/3x-6|+C x² + 5x + n/x-21 +C 2 3 In Evaluate the…

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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…

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: 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: S 1 Solve the integral: √√√X = n/1+x²³²|+c A C {/in/1+x²³ | +c B © 6n/5+x²³²|+c C in/1+x³| +c D X +…

A:

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

Q: Question 16 d If g(x) = == S[e²-In (21+1) ]dt, find g(x). dx 4 A et + (2x+1)2 e* -In(2x+1) 4 e¹+ (2x…

A: We will first find g(x).

Q: To evaluate the integral sin³0cos ede by trigonometric transformation, we use the identity; 1-cos20…

A:

Q: s (x+1) log(x+1)

A:

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

A: To solve this problem we use cylindrical shell.. method.

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: A detailed solution is given below

Q: Evaluate the improper integral 3 -2 X -dx

A:

Q: If $S₁ A B (x+1) dx (x+2)(x−1)² 9 3 D -la 1 9 I -ja 2 3 2 93 12 93 ==√ [= ²4/2+1 B x-1 C (x-1)² ]dx…

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Q: Evaluate the improper integral (A) diverges B (Q) Na O ساح 3 1²23 -dx

A:

Q: Question 37 1 Solve the integral: S- dx √√√√x+x A m/1+ + X +C ℗ 6n/5+x²³| +C B Ⓒ1+x²+c с X C =…

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Q: Given S dx, determine all value/values of for which the improper integral XP converges? (A) {0,1} B…

A: Please follow the next step.

Q: The improper integral A B if the 0 1 0 e dx is

A:

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

A:

Q: Question 9 d If g(x) = ·S*^[e'− In(2t+1)]dt, find g''(x) . dx -2 4 A (2x + 1)2 4 B (2x + 1)²…

A: Using leibnitz rule.

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

A:

Q: Determine the area bounded by f(x)=x²-x and x-axis. A unit² -unit2 unit² |+ B 2 © ½ u Ⓒ / unit ² D…

A: Let's find area of given curve.

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 -…

A:

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

Q: Evaluate the triple integral: A 24 B 6 12 18 √₁³√₁² √²(x + y + (x+y+z)dydxdz

A:

Q: We can apply General Power Formula of Integration on which of the following integrals? (A) Jeschuco…

A:

Q: To evaluate the integral sin ³0cos 0d0 by trigonometric transformation, we use the identity; A…

A: ∫sin3θcos6θ dθ

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

A: To find the solution for integral

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…