Question 6 Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1, A unit² Ⓡ® 3/unit² B Ⓒunit² Ⓒ / unit² D

Q: Evaluating √√9-x² dx using trigonometric substitution will (A) 18 18 [*/2 cos²0d0 0 **/2 B 0 Cab…

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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: (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: tanx f f(x) = = [tion. A B C √1+1² 1+e' In (secx)√1+tan²x tanx 1+e sec²x 1+ e tanx sec ³x tanx 1+e…

A: Integration

Q: •+∞0 The improper integral * fe 0 A) 0 B e C (D) 1 ∞ ex dx is

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

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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 -aluate: A…

A: Topic:- application of integration

Q: Question 12 Given S (A) (-∞0,00) B (1,00) D -dx, determine all value/values of P for which the…

A: Here we have to determine all values of p of the given improper integral in which the integral is…

Q: dx using miscellaneous substitution will yield to secx + 1 Transforming Ⓒ S A 1-z² B 1+z² © √ 1 +…

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

A: Option (B) is the correct answer.

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

A: Solution: Natural length  = 3 ft   ---> 18 ft-lb 3 ft to 6 ft

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

A: To find integrand the steps are as follows.

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

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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: d If g(x) = - S* [e'− ln(2t+1)]dt, find g''(x) dx -2 2 A ex. (2x + 1)² 4 (В B et + (2x + 1)² Ⓒe*…

A: Given that gx=ddx∫-2xet-ln2t+1dt

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: Question 11 puas √1+1² Ffxx)=f -dt, then f'(x) equals 0 I+e' In(secx)√1+tan²x Itela tanx sec³x 1+ele…

A: Topic:- application of integration  Note :- as per our guideline if more than one question uploaded…

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: 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: A lighthouse is on an island 400 meters off shore. The lighthouse beam makes a full turn every 15…

A: answer is in next step

Q: B C) + et. + 4 (2x + 1)² 4 (2x + 1)²

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

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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: Evaluate the improper integral A 0 (B 4 C diverges 2 D 9 mit 2 3 -2 X 3 dx

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Q: 4 Evaluate the double integral: 2ydydx 1 A B (ⒸⒸC) D m 100 8 +10 9 2 5 2

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

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

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Q: Given 1 [₁f(x) dx = 0 and -1 1 S²F(x f(x) dx = 11 6 I evaluate 1 √²3f 3f(x) dx - .0 -1 2f(x) dx.

A: Explained below

Q: Find the volume of solid generated by revolving the region bounded by g(x)=x²+2x+ 5about the x-axis.…

A: Given:      fx=x2+1      gx=-x2+2x+5  Volume of solid revolving around the region is…

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

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Q: dx Transforming - using miscellaneous substitution will yield to secx + 1 A -dz 1+z² B 1² 2-2z² 1+z²…

A: Given problem:-

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: 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: 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: d [e'- In (21+1)]dt, find g(x) . dx -2 A ex-In(2x+1) 2 B ex_ (2x + 1)2 4 C (2x + 1)² 4 D (2x + 1)²…

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Q: 1 Solve the integral: J 3 x + x 5 6 x In|1+ A +C + C Shi+x+c 6 1+ C 5 1+x8 +c +C B C 516 In|1+ - 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 (e²+ 1)² e2 (e³-1)²…

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Q: Evaluate the double integral: A B NIG 5 3 m|p 99 In +10 2ydydx

A: To solve the following double integral

Q: 1 √√√√√x + x S Solve the integral: 5 @ =³√√/1+ x ³²³/ + C A {m/1+x²³² |+c ==ınlı 5 6 B C ©…

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

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Q: Evaluating ³√9-x² dx using trigonometric substitution will lead to: 15/2 A cos²0d0 B 18 cos²0d0…

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Q: Given B ₁ [_²_f(x) dx = 0 and [ f(x) dx = 11 2 55 6 D 0 11 11 = √²3f(x) dx - _2f(x) dx. evaluate

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Q: √√ Solve the integral: √√x A (В 33√x² +C Ⓒ 3√/x² +6 +C D 6√√x +C √√x dx x²

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Q: Determine the area bounded by the functions f(x) = (x+1)³ and g(x)=x+1, 3 (A) Žunit² 1 -unit² -unit²…

A: We need to find area.

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

A: Ans: C

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

A: If fx and gx are integrable on the closed interval a, b, and k is a constant, then to determine wich…

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: 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.