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

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 (e²-1)²…

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Q: y = 3t 1+t³ X= 3t 31² 1+t²³

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

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Q: A balloon is released fromthe ground 100 meters from an observer.The balloon rises directly upward…

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Q: Given the integral sec6 (x − 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: The given integral,       ∫sec6x-1tan4x-1dx

Q: ff. W Ex] Let f(x) = 4x²+2x²+x+3 and :f(x), g(x) € 75[x] f(x). g(x). g(x) = 3x² + 3x²³² + 3x² + x…

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Q: 3) x² + y² + 16x+10y+80= 0

A: Given

Q: the integral: (u +3) du 1²5 -dx (3) √74³ cscxcotxdx

A: We have to find out integral

Q: Question Find the average value of f(x)=√x-8 over the interval [0, 2]. Submit an exact answer using…

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0 A) infinitely many B) may…

A: We need to choose correct option.

Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: 0 ✓1+13xdx

A: Given that ∫021+13x3dxSolution:let 1+13x=t313dx=3t2dtdx=3t213dtat x=0,t=1at…

Q: Please show work in terms of d(variable)/dt, thank you! Water stored in an inverted right circular…

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Q: (x²-3x+1) dx

A: Given that ∫23x2-3x+1dxSolution :∫23x2-3x+1dxx33-3x22+x23333-3322+3-233-3222+2

Q: x³-8 4 x+2 x 16 2. lim

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Q: ,3 Which of the following can be determined given f(x) dx = 5, g(x) dx = 7, and ,3 [³h(x) d h(x) dx…

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Q: Question 11 If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant,…

A: Topic:- application of integration

Q: What is the range of the function y = 5 sin(0+ 60°) - 4? O -60° ≤ y ≤ 60° O-9≤ y ≤ 1 O-4≤ y ≤9 O-1 ≤…

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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 & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

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Q: In 1991, there were 41,144 shopping centers in a certain country. In 2001, there were 48,157. (a)…

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Q: Evaluate the double integral: (A) 40 B 30 C) 60 D) 80 ²(3x² +9y²) dxdy

A: The integration are.  .

Q: (x²-3x+2) dx

A: Please see the below picture for detailed solution.

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

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Q: antiderivatives does a function of the form f(x)=x" have when n*O? may vary depending on n How many…

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

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

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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…

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Q: y = x^Arctan *(x4)

A: We have to solve derivative

Q: L₁ |x|dx

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Q: J (u-2) (u+3) du

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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: L²x√x-2dx

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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: Find the derivative of the function at Po in the direction of u. x-y g(x,y)= xy+2 Po(1,-1), u=12i+5j…

A: Given :g(x,y)=x-yxy+2u=12i+5j

Q: ร n=1 6 : 2n-1 3h

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Q: Which point is the center of the circle * 4x² + 4y² = 4y - 8x + 5? (-1,-/-) (1,-1) 2 2 Option 1…

A: This question is based on general equation of circle.

Q: Question 2 Solve the integral: A √√x 3 B 33√/ x² +C 3√x² +C 6 6√√x +C D √√ 3√x dx

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Q: Find the value of x If f'(3) = 52? X 1 2 4 f(x) -2 8 x

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Q: 6) (-2√√2, 2√2) 8) (2 3 3√3 2' 2 10) (-2,-2√3)

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Q: 2 1) x² + y² + 18x - 26y +246=0

A: Topic = Equations Only question 1 is answered , As per asked by student.

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: Question 1 Solve the integral: Seln(2x²+3x-4)³ (4x+3)dx A eln(2x²+3x-4) (4x+3) 3(2x²+3x-4)…

A: To evaluate the given indefinite integral.

Q: 16. J x² 4 + x² dx

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Q: |x-4|dx

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0₂ (A) 1 (B) none may vary…

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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: y = tan e³x + etan3x

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

Q: --—-^[e'-In(2t+1)]dt, find g''(x) . dx -2 If g (x) = (A) (В Ce*- D 4 (2x + 1)² e* - In (2x + 1) 2…

A: We have to solve integral

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

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Q: d) S tanrd. cos³x

A: