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 10 log² (x + 1) + C 2 In 10 In [log(x+1)] + C

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: dx (x+1) log(x+1) ¹__In[10g(x+1)]+ C In 10 - - log² (x+1)+C 2 -In10 log² (x+1)+C 2 In 10…

A: On solving this we will get Option (D) is correct

Q: 15 S A B (c) D (x+1)dx (x+2)(x-1)² 1 2 -- 9 1 2 " 9 3 -lo 1 9 " - - W|N 2 1 9 3 W|N 3 -S[₂ = A B +…

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Q: 14. Evaluate [4³x dx 3x O 4³x 3x +C 6ln2 O 4³x In4 O 43x+1 3x+1 +C O None of these +C

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

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Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: dx ·S (x+1) log(x+1) Evaluate:

A: Given that,

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: The limits of integration will be the interval on the x-axis for which the area is bounded.

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 A B с D f(x) dx = 0 and [ f(x) dx = 11₁ -1 11 6 55 6 0 11 5 - S²3f(x) dx - √₁2 f(x) dx.…

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

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

A: A option is correct.

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

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Q: etermine the area bounded by f(x)=x²-x and x-axis. 1 A unit² 2 B unit² 1 unit² 1 unit² D

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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: 1 S dx 3 x + x Solve the integral: 5 A + x +C 1+x+c n 1+x+c in 1 B + x + C © 6/5+x²³/+c C ® 1+x+c In…

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

A: To solve the following problem

Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² − 4 = 0, using a vertical element.…

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Q: dx 15 √(x+2)(x-1)²² -S[ +42 + (A) 93 B (C) (D) 12 93 —— . 2 3 2 3 B x-1 + (x −1)² ]dts dx, the…

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Q: dx using miscellaneous substitution will yield to secx + 1 Transforming S Ⓒ √ ²² +²2 dz (Α) -z²…

A: This question can be solved by substituting z=tanx2

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

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Q: en 0 3 | f(x)dx=0 and. -1 S 11 11 5 55 6 f(x) dx = = 11 6 , evaluate 1 J 3f(x)dx - [2f(x)dx.

A: We will distribute the integral in two parts .

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: Integration

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: dx (x+1) log(x+1) 1 -In[log(x+1)] + C In 10 -In 10 log2 (x+1)+C 2 In 10 In[log(x+1)] + C 1 Evaluate:…

A: To solve the following problem

Q: d If g (x) =-=-^[e'- In(2t+1)]dt, find g''(x) . dx -2 A ex-In(2x+1) 4 B et + (2x + 1)2 4 (2x+1)2² 2…

A:

Q: for Which of the following can be determined given S √₁² f(x)dx = 5,³ g(x) dx = 7, and d Ⓒ [[²(f(x)…

A: ∫ab fx±gx dx =∫ab f(x) dx ±∫ab g(x) dx ∫ab kf(x) dx =k∫ab f(x) dx ; where , 'k' is an constant.

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

A: The region bounded by line y = x - 1 and the curve y = (x - 1)3 is as below

Q: Find the volume of the solid generated using washer method by revolving the region bounded b y = x²…

A: Let's find volume of solid by using washer method.

Q: 2) Find the standard deviation of the population sample. 2, 4, 7, 12, 15 3) Find the variance for…

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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: 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: Question 15 Evaluate the double integral: (A) 40 B) 80 C) 60 (D) 30 ²² 6) (3x² +9y²) dxdy

A: we can find the double integral.

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

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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: B $S₁ (x+2)(x-1)² = √[=42+²1+ (-₁2). (x 1)² ]dx, 1 x-1 A B C If -io 9 -ja -ia 2/3 1 2|3 2/3 2 the…

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Q: If (A) (В (D (x + 1) dx (x+2)(x-1)² -ja دا | در 93 1 —— 9 9 . 3 2 3 x + 2 ++ x-1 (x-1)2 dx, the…

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Q: Determine the integral: x²cosxdx A x²sinx-2xcosx-2sinx + C B x²sinx + 2xcosx-2sinx + C x²sinx-2xcosx…

A: Integration

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: Let f(x)=√√3x-2 axis about the y-axis and find the volume of the resulting solid. 43x A -unit 3 135…

A: Ans: C

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: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx

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Q: Determine the area bounded by the functions f(x) = (x + 1)3³ and g(x)=x+1₁ A unit² B unit² 3 Ⓒunit²…

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Q: (в B f(x)g(x) dx = [ f(x) dx g(x) dx]

A: