If f (x) = A) B (C) D tanx √1+1² 1+e' 0 1+tan²x tanx 1+e sec ³x -dt, then f'(x) equals tanx 1 + e In (secx) √ 1+tan²x 1+ e tanx sec²x 1+elanx

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: (x+1)dx (x+2)(x-1)² 2 . 93 15 S If (A (B) (c) D -- 9 9 9 2/3 W|N 3 A = -√ [14/2₂ B + x+2 x-1 +…

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

A: On solving this we will get

Q: en [_²_f(x) dx = 0 and ² fl Given f(x) dx = 11 6 T evaluate √3f(x)dx- -S__2f(x)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: 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: Determine the case of the following proper rational function after simplification: x + 2…

A: We have to find out simplification

Q: Solve the integral: Seln(2x²+3x-4)³ (4x+3) dx (2x²+3x+4)¹4(4) A + C 3 eln(2x²+3x-4)³ B + C…

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Q: Evaluate the integral: Se³+ cosh2x33+ cosh2xsinh2x dx 3+ (3e)3 + cosh2x A + C 2+2ln3 (3e)3 + sinh2x…

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

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

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Q: solve the following differential eqaution : (2x+y)dx-(4x+2y-1)dy=0

A: Solved below.

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

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Q: How many antiderivatives does a function of the form f(x) = x^ have when n0? (A) 1 B) none (C)…

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Q: Solve the integral: A B C D 6√√x +C 3√x² + C 6 33³√/ x² +C √√√x 37 ကြ 3√x dx

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

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Q: Solve for x using Newton-Raphson Method: e-x-x =0 Use xo=0 as an initial guess.

A: We have to find the next approximate newton rapson formulae.

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

A: Please see the below picture for detailed solution.

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

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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: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ unit² ® -unit² Ⓒ unit² 3…

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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: 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: 1 m ( x² + 3102=²7) dx x²+3x-7 X-2 Evaluate the integral: Se A +2²2 + — + In|3x-6√ + C Ⓡ X/²2 ₁ B…

A: A detailed solution is given below.

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

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Q: Transforming S Ⓒ / ² A 1-z² 1+z² ® / 12-2 B 1+z² © Ⓒ S ²¹²+² dz 1-z2 1+z² D S 1-z² dx secx + 1 -dz -…

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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 integral: x²cosxdx (A) x²sinx+2xcosx-2sinx + C (B) x²sinx-2xcosx+2sinx + C…

A: topic- indefinite integral

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

A:

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: A detailed solution is given below

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

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

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

A: Always false

Q: 9 Let the integral be solvable' using trigonometric substitution. What is the correct choice of u…

A: A detailed solution is given below.

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x) =…

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

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Q: Determine the integral: [x²cosxdx

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

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

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Q: feschucoshudu cschusinhudu sinhucothudu cosh coshu sinhudu O fir

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Q: 3x e 1+e³x 13. What is the best substitution to make to evaluate S O u = 3x Ou = e³x Ou=1+e³x O u =…

A: A detailed solution is given below.

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

A: We can solve this as follows:

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)=x²+2x+…

A: Let's find volume of solid.

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

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

A: To integrate the following problem

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

A: