Evaluate the triple integral: 3 ₂2 0 (x+y+z)dydxdz

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

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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: The integration are

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

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

A: We can solve this as follows:

Q: Determine the area bounded by f(x) = x² - X and x-axis. A -unit² uni B unit² 1 -unit² C D -unit² 2 3…

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Q: Given A B D [ f(x) dx = 0 and -1 7 55 11 5 1 √ ² f(x) dx = 11 evaluate 0 √²3f(x) dx - dx-₁2f(x) dx.…

A: Solved below.

Q: Question 10 tanx If f(x)= A (B) C D sec ³x Itelin sec²x Iteline 1+1² I+e' -dt, then f'(x) equals…

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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: limit of integration

Q: Evaluate the triple integral: A) 6 B) 18 C) 24 D) 12 3 2 1 ²³√ [²√ √ 0 (x+y+z)dydxdz

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Q: Solve sin² C cos²x = 1 on the interval 0 < x < 2T. -

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Q: 17. Evaluate [9e³x dx O9e³c+1 3c+1 O9e3c O9ec-3 3e³c-3

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

A: The integration are

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 3 A 2/2 unit² А 3 B -unit²…

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Q: To evaluate the integral [ sin³@cos³0d0 by trigonometric transformation, we use the identity; 1 +…

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Q: ral: Seln(2x²+3x-4)³ (4x+3)dx

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Q: Find the area bounded by : f (x) =e*, g(x)=e¯* and x=3. A (e²-1)² e² sq. units (e³-1)² e3 sq. units…

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

A: the point of intersection of  y=x-1 and y=(x-1)3  and y=0 are (0,-1),(1,0) and (2,1) the line…

Q: Evaluate the line integral, where C is the given curve. Lexy² ds, C is the right half of the circle…

A: Solution: I=∫cxy4ds

Q: Given √ 1 pdx.c A (-∞,1] B (1,00⁰) Ⓒ (-∞0,00) D (0,1) dx, determine all value/values of P for which…

A: This can be solved as follows:

Q: y = x^Arctan *(x4)

A: We have to solve derivative

Q: Question 17 The improper integral A 00 B) e C) 0 (D) 1 if the 0 edx is

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

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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: (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and…

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

A: We have to find out the solution

Q: . Evaluate 1 4-x² dx

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

A: Always false

Q: e integral: J √√√x+x F1+x X + C 1 x C 5 + C 6in|5+ x² +C 6

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

A: We have to choose correct option

Q: 9. For what value of k, k> 0, does (4kx-5k) dx = k² O 1 O 2 3 O 4

A: On solving this we will get

Q: dx aluate: :S₁ (x+1) log(x+1) A In10 In[log(x+1)] + C 1 B -In[log(x+1)]+C In 10 O In 10 log² (x + 1)…

A: Topic:- application of integration

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

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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: --—-^[e'-In(2t+1)]dt, find g''(x) . dx -2 If g (x) = (A) (В Ce*- D 4 (2x + 1)² e* - In (2x + 1) 2…

A: We have to solve integral

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

A: Solved below.

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: 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: If f(x) = A B (C) tanx S 0 sec ³x 1+e tanx 1+tan²x 1+ e tanx 1+12 sec²x 1+e tanx In (coor) 1+ e'…

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

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Q: Evaluate the improper integral (A) diverges (в B (C) ml+ 2 3 √√2²233/3dx 4

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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: Determine the area bounded by the functions f(x) = (x+1)³ and g(x)=x+1. 1 A unit² ® 2-unit² B 1…

A: Please see the below picture for detailed solution.

Q: x+2 Determine the case of the following proper rational function after simplification: (x²-4)(x³-8)…

A: The first problem is related to simplification and second one is related to linear composition.

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: Question 27 Determine the area bounded by f(x)=x²-x and x-axis. A —-unit² А B unit² Ⓒunit² D unit²

A: A detailed solution is given below.

Q: (x+1)x (x+2)(x-1)² If f @ 1/1 1/1/0 93 B C D 9 . - 2 3 2 9 3 - 2/3 . 93 A B 421 + + x+2 C (5-131].…

A: Explained below

Q: Evaluate the double integral: A B D) 9|N 2 N|G m 100 3 8 •√x 1. √ √V 24 +10 2ydydx

A: Evaluating the double integral

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

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Q: X+2 Determine the case of the following proper rational function after simplification: (x2 -…

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