Given [₁₂f(x) dx = 0 and A 0 B Ⓒ D √ √ ² f(x) dx = ²1 55 11 11 5 11 6 " •√²3f(x) dx - √₁2f(x) dx. evaluate

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A: find out the work required fo stretch the spring an additional 3 ft.

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A: To solve this problem we use washer method.

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A: Formula: Antiderivative of xn = xn+1/n+1

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.

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A: Note: According to our expert guidelines only first individual question is to be answered kindly…

Q: Transforming - Ⓒ S 1 = ²2²1dz 1+z² ℗ B / 1 + 2/2 d -dz 1-z² Ⓒ *2-2z² 1+z² (A) dx secx + C-²₁- -dz…

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Q: feschucoshudu cschusinhudu sinhucothudu cosh coshu sinhudu O fir

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A: (tan x)' = sec2(x) (eax)' = a eax.

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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…

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A: Solved below.

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Q: Question Evaluate the indefinite integral given below. Provide your answer below: f(sin³(x)-3…

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A: Ans: C

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:

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*O₂ A infinitely many B may…

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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: 16. Evaluate O 1 O 2 3 O 4 8 X ²+36 dx

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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:…

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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

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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

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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: 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: (x+1) dx (x+2)(x-1)² = √ [+²2 S₁ B + - - 1 + x-1 (x-1)2 ]dx. the values of A & C respectively are:

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Q: Question 3 In the indefinite Integral in(cosh. x +ex). sinh x +e* (A cosh x + ex sinh x + ex In(cosh…

A: The integration are

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

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

A: We have to choose correct option

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: Which of the following is NOT a method for finding volume of solids of revolution?

A: answer is in next step

Q: If g(x) = d __*[e' - In(2t+1)]dt, find g''(x) . dx -2

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Q: f 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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