Question 7 Evaluate: A B с dx (x+1) log(x+1) In 10 In [log(x+1)] + C 1 -In[log(x+1)] +C In 10 -log² (x + 1) + C

Q: (6x5+2x) dx

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Q: (2x³ + 5x-4) dx

A: Solved below.

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

A: We can solve this as follows:

Q: dx secx + 1 Transforming - -z² A 1+z² B z²+z 1-z² 1+z² Ⓒ 1- D √ -dz -dz -dz - 2z² 1+z² -dz using…

A: Here, the given integral is: I=∫dxsec…

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

A: Given, ∫ 9/√(x2+6x-7) dx We can calculate using substitute method

Q: 17. Evaluate [9e³x dx O9e³c+1 3c+1 O9e3c O9ec-3 3e³c-3

A:

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

A: To find the volume. Option B is correct.

Q: Evaluate the definite integral by substitution: 21 1 dx 3/(1+3r)² (1) ² 3/1 + 13xdx 10 (3) [TV. (3)…

A:

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: [/2cos²0do (A) 18 9[*/ cos²0d0 B…

A:

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: e: Sz dx (x+1) log(x+1)

A:

Q: A lighthouse is on an island 350 meters east of the shore of Lake Nathan. The lighthouse beam makes…

A:

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

A: We have to find out the solution

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

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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: Find the domain of the following function. 9 f(x)=- 2 36-x The domain is (Type your answer in…

A: Use the definition of domain of function

Q: Fin the AREA enclosed by the given curve: r=acos(3θ)

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Q: A plane flies at a speed 580 km/hr at a constant height of 12 km. How rapidly is the angle of…

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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: Draw a graph to match the description given. f(x) is increasing over (-∞o,-5) and decreasing over…

A:

Q: A lighthouse is on an island 500 meters off shore. The lighthouse beam makes a full turn every 9…

A: A lighthouse is on an island 500 meters off shore. The lighthouse beam makes a full turn every 9…

Q: (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and…

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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: 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 sq.…

A: The region bounded by the curves f(x)=ex, g(x)=e-x and x=3

Q: Determine the area bounded by f(x) = x² - X and x-axis. A -unit² uni B unit² 1 -unit² C D -unit² 2 3…

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Q: Solve the integral: 1 √√√√√x+x dx

A:

Q: dx S using miscellaneous substitution will yield to secx+1 z²+z 1-z² 1+z² 1-z² -z² 1+z² Transforming…

A: solution

Q: y = x^Arctan *(x4)

A: We have to solve derivative

Q: Determine the area bounded by f(x)=x²-x and x-axis. A unit² (В B (c) unit² D unit² w|m 16 H|4 unit²

A: Given that we need to find the area bounded by f(x) = x2 -x  and x- axis.  Now,

Q: A 60m climbing rope was used in a tall building. How much work is performed in pulling the rope up…

A: Force function need to be constructed and then work done is calculated.

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

A:

Q: In S₁² = 10 A (1,00) B (-∞0,00) c) (-∞,1] D {0,1} Given -dx, determine all value/values of P for…

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Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

A:

Q: πT Evaluate the integral: S sin(3x)cos(3x) dx

A: We can solve this as follows:

Q: 0 ✓1+13xdx

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

Q: Determine the area bounded by  f(x)=x^2 -x and x-axis.

A: Explained below

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

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Q: (b) En=1 m

A:

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: After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the…

A: answer is in next step

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…

A:

Q: dx Evaluate: s (x+1) log(x+1) A --In 10 log² (x+1)+C 2 B In10 In[log(x+1)] + C с = -log² (x + 1) + C…

A:

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: 10. Prove the identity: 2 + cot² (x) _ 1 = sin² x - csc² (x)

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Q: Suppose that cote = c and What does sin equal in terms of c? O sin = √1+c² O 1 sin = √1-c² O sin =…

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Q: Evaluate the following integrals using (a) Trapezoidal Rule and (b) Simpson Rule by finding such…

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

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Q: (1) Estimate the area under the graph of f(x) = 1/x from x= 1 to x=2 using five approximating…

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Q: Give the domain and range. Then, use the graph to find (a) f(-2), (b) f(0), (c) f (9) 1 (2) Ay Q 40…

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Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vfl(-12,-2)=i+j+k (Type integers or simplified…

A: Given