Question 31 Evaluate the integral: A B C D H|m 1 1 13 1|6 sin(3x)cos(3x) dx

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…

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Q: Evaluate the integral: A B C D 16 1 "Im =|m 1 7/6 دان داww 3 sin(3x)cos(3x) dx

A: We have to find out integral

Q: Evaluate the triple integral: (x+y+z)dydxdz A) 18 B) 24

A: ∫03∫02∫01(x+y+z)dydxdz=∫01(x+y+z)dy=xy+y22+zyUpon substituting=x+0.5+z-0=x+0.5+z

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

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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: tanx -√ S sec²x 1+ et tanx In (secx) √✓ 1+tan²x 1+ elanx sec ³x 1+etanx If f(x) = A B (с 1+1² 1+e'…

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Q: X √√√3/2 x² Solve the integral: A 6√√x +C 3√√x² (B - + C 6 Ⓒ3√√√x² +C с √x (D 3 dx

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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: (x + 1) dx (x+2)(x-1)² 15 S= = √ [ +42 A B + x + 2 x-1 C + + (x-1)2]dx. dx, the values of A & C…

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Q: 3. Use two rectangles of equal width to estimate the area between the graph of f(x) = x + cos(x) and…

A: Solved below.

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: +∞o fthe 0 The improper integral edx is

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

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

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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: Given A) B (C) D 11 √ √ ² f(x) dx = = /10 f(x) dx = 0 and 11 6 20 55 •[ 37/(x)dx - 5² 2/(x)dx…

A: D option is correct.

Q: Solve the integral: A B D 3√√√x² +C 6√x +C + C 6 √x 3 3√x dx

A: We have to solve integral

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: [/2cos²0do (A) 18 9[*/ cos²0d0 B…

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Q: (x+1)dx (x+2)(x-1)² 1 / S If B -√2-1 + + *(x-1)2 ]dx. +2 dx, the values of A & C respectively are:

A: We can solve this as follows:

Q: Evaluate

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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

Q: Which of the following can be determined given ,3 3 ,3 [ f(x)dx = 5, [_g(x) dx = 7, and [ n(x) dx =…

A: To determine the given integral.

Q: Solve the integral: A 5n/1+x²|+C 5 (B) 6in 5+x' 6In|5+ +C 음 m/1+x²|+c C ³√|+C 1+x √√√√x+x² dx D

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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: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

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Q: Given √√2/10 dx, determine all value/values of P for which the improp хр onverges? A) {0,1} B)…

A: Topic:- application of integration

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

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Q: 16. Evaluate O 1 O 2 3 O 4 8 X ²+36 dx

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x +1. 1 A = unit ² B 3 2…

A: Determine the area bounded by the function f(x)= (x+1)3, g(x)= x+1 .

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…

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Q: f(x)=√3x-2 on the interval Let of the resulting solid. 83 (A) -unit 3 135 43x B -unit3 125 83x…

A: Ans : A

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

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

A: We have to choose correct option

Q: (x + 1) dx A (x + 2) (x− 1)² = √ [ +42 + 15 S B + x-1 C (x-1)² dx, the values of A & C respectively…

A: answer is in next step . please give a like !!!

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

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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: 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 ©…

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Q: dx secx + 1 Transforming S Ⓒ 1 +²2² A 1-z² (В) / z²+z 1-z² 2-2z² © 1+z² -z² Ⓒ S 1=32/2/dz D 1+z² -dz…

A: Solve using miscellaneous substitution

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: 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: Question 32 Solve the integral: A) 3√√√x² +C (B) ex 3 2√x² +C с D 6√√x +C 3√x x² dx

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

A: The integration are

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

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

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Q: e the integral: S- 1 √x © $ n/²+x²³/+c +C © ²0/₁+x²³²/+c\ +C == n/₂+x²³/+c +C √x+x dx

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Q: $²² Α) (1,∞0) B (-∞,1] (-∞0,00) Given D {0,1} dx, determine all value/values of P for which the…

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Q: Practical Question: An object is moving horizontally with the speed of 50 m/s. When the object at…

A: Projectile motion is the motion of an object projected horizontally into the air and moving…

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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