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

Q: 1 3√x + x X Solve the integral: J 6 5 F1+x8 + c A @ c in 1 B 1+x + C © n1+x.c C C Gin|5+x²|+C D - dx

A: Explained below

Q: 1. Write the explicit formula for the sequence. Then find the fifth term in the sequence. a₁ = 120,…

A: Considering the sequence to be geometric

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

A: We have to find out integral

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: To evaluate the integral sin ³0cos 0d0 by trigonometric transformation, we use the identity; A…

A: ∫sin3θcos6θ dθ

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: 1 H 0 1 2 3 4 5 6 What are the domain and range of its inverse? O Domain: {y|1 ≤ y ≤5, ye R} and…

A: The domain of a function f(x) is the set of all possible values of x for which f is defined. The…

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: Question 20 How many antiderivatives does a function of the form f(x)=x" have when n*0₂ (A) 1 (B)…

A: Antiderivative means Integration

Q: 1 x + × olve the integral: 5 ® shi+x+c A C 5 6 ® $h1+x+c B C © 6n|5+x²|+c C D Shi+x+c C dx

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Q: Question Find the average value of f(x) = -3 cot (x) csc (x) + 1 over the interval [3 Submit an…

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Q: dx using miscellaneous substitution will yield to secx + 1 Transforming S Ⓒ √ ²² +²2 dz (Α) -z²…

A: This question can be solved by substituting z=tanx2

Q: 3. Evaluate the integral: (1) (u-2)(+3) du @[²7/1 dx (3) rπ/3 cscxcotxdx

A: topic- definite integral

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

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Q: Question 27 Evaluate the double integral: (A) 80 B 30 с 40 D) 60 Question 28 Questions Filter (40) Y…

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

A: Integration

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

A: To find the work done.

Q: 2 Let f(x)=√3x-2 on the interval 1 1. Revolve the region between the curve, y=1 and y-axis about the…

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

A: To find the solution for integral

Q: y=1/x²₁ y = 8x₁ y=x/8

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Q: 1 1 11 f_²_f(x) dx = f(x) dx = 0 and f(x)dx [² f(x) dx = 1 1 ₁ 6' 1 0 [²3F(x) dx - √ 2P(x)dx -1 11 6…

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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…

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Q: . Evaluate 1 4-x² dx

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Q: Solve

A: We have to calculate the given indefinite integral

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 3 A 2/2 unit² А 3 B -unit²…

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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: 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: (6x5+2x) dx

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Q: Use Disk Method to find the volume of the solid generated by revolving the R bounded by y = x, y =…

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Q: dx √81+16x² S

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Q: 3 2 1 Evaluate the triple integral: S (x+y+z)dydxdz (A) 12 B) 18 24 (D) 6

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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: Evaluate the line integral, where C is the given curve. Lexy² ds, C is the right half of the circle…

A: Solution: I=∫cxy4ds

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: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 [*1/2 cos²0de A 0 Ⓡ IS!" B 18…

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Q: Evaluate the double integral: S²² (3x² +9y²) dxdy 0

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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: 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: b. Solve the following initial value problem for y as a function of x for differential equation x-2…

A: The objective is to solve the differential equation.

Q: 14. Evaluate [4³x dx 3x O 4³x 3x +C 6ln2 O 4³x In4 O 43x+1 3x+1 +C O None of these +C

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

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Q: U 4. Let f(x, y) = ey, where x = uv, y = a) Use chain rule to compute and af af Əv ди b) Express…

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Q: L₁ |x|dx

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Q: If 8(x) = [e²-m (21+ - dx S[e²-In (21+1) ]dt, find g(x). -2 A e-In(2x+1) 4 B (2x + 1)² 2 Ⓒ (2x + 1)²…

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Q: (1) y=x, y=2-\x/ (2) y=1/x², y = 8x, y = x/8

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Q: X-2 dx Evaluate the integral: Sein(x²+3x-7) A x²+5x+In|3x-6|+C B ++ In|3x-6|+C 2 5 © +²2+5x+In/x-21…

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Q: ion 8 apply General Power Formula of Integration on which of the following sinhucothudu cosha coshu…

A: We have to choose the correct option from the given options

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: