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 J

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 B e3 (C)…

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Q: luating√√9-x² dx using trigonometric substitution will lead to: **/2 sin²0d0 3 of th 9[*/ cos²0de…

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

A: Correct option is missing

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

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

A:

Q: A solid is formed by rotating the area between the curves y = x and y = x² between x = 0 and x = 1…

A: To solve this problem we use washer method.

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: 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: 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: 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…

A:

Q: Evaluate the improper integral 3 A 4 B) diverges C D —— 6/0 m|+ ² 0

A: Topic:- application of integration

Q: Which of the following is NOT a method for finding volume of solids of revolution? A) washer method…

A: Conic 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: Given problem:- If a horizontal element is used to find the area bounded by y=√x, x=4 and the…

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

A:

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: Find the are bounded by the curve y = x and y = x^2 - 2. * 2/9 sq unit 9/2 sq. units 16/3 sq. units…

A: Use the intersection of the curve and then integrate the upper curve minuses the lower curve to find…

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

A:

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

A: Given that g(x) is a differentiable function and range of g(x) is interval I. f(x) is a function…

Q: tanx If f (x) = A B C D f √1+1² 0 1te¹ In (secx)√1+tan ²x 1+ e tanx 1+tan²x tanx 1+e sec 3x 1+ e…

A:

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

A:

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

A: To find the area bounded by curves

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

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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 ©…

A:

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

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

A: The given expression is:…

Q: Solve the integral: A In/1+ B -In|1+ x 5. 1 3X + C + C 5 x X + X x dx

A:

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

A: integration

Q: If f(x) = (A) B C D tanx sec ³x 1+e 1+1² 0 sec²x 1+ e tanx In (secx)√√ 1+tan²x tanx 1+e 1+tan²x 1+ e…

A:

Q: In the indefinite Integral in(cosh x + e*). sinh x + ex cosh x + ex dx, what is the integrand?

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Q: To evaluate the integral si sin³0cc 1³0cos 60d0 by trigonometric transformation, we use the identity…

A:

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

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Q: Please write out/show work, thank you! Find the slope of the line tangent to 2xy + π sin y = 2π…

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Q: 腰 √√/XX S₁ Solve the integral: A 3√√√x² + C √√x² (B) + C 6 Ⓒ6√√x +C dx

A: ∫x3x2dxRewrite:=∫1x56dx

Q: aluate the integral [ sin³0cosº0d0 by trigonometric transformation, we use the identity; 1+ cos20…

A:

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

A:

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: 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'…

A:

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

A: We need to choose correct option.

Q: If g(x) = -S^*[e²− ln(2t+1)]dt, find g''(x) . dx 2 (A (2x + 1)2 Be* -In(2x+1) 4 (C) Ce¹+ (2x + 1)² 4…

A: Here is the solution of the given problem.  By using derives under Integral.

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

A:

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: Evaluate the double integral: 2ydydx A 4 9 B) m 100 8 NIG 2 9 2

A: To find the value of given double integral.

Q: Question 5 The improper integral +∞0 5+0⁰ 0 ex dx is

A: We can solve this as follows:

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: Given A (В B [²₁f(x) dx = 0 and 11 6 11 5 55 6 √ √ ² f(x) dx = 11 6 0 evaluate 0 [²3f(x) dx - ₁2f(x)…

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

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Q: √²/pdx. хр (1,00) B {0,1} C) (-∞0,00) D (-∞,1] Given (Α dx, determine all value/values of P for…

A: