Evaluating √9-x² dx using trigonometric substitution will lead to: -3 A 355/20 cos²0de 0 **/2 B Ⓒ 18 18 0 **/2 0 cos²0de sin²0d0 cos²0d0 **/2 0

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

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Q: Evaluate the improper integral (A) diverges (в B (C) ml+ 2 3 √√2²233/3dx 4

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

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Q: Solve

A: We have to calculate the given indefinite integral

Q: 3. 2y"" − 3y" – 3y² + 2y = (e*+ex)²

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Q: Evaluate: A B С) D (x+1) log(x+1) 1 -In[log(x+1)] + C In 10 1 -In 10 log² (x + 1) + C 2 In 10…

A: Given problem:-

Q: Consider the vector field. F(x, y, z) = (9ex sin(y), 2e sin(z), 4e² sin(x)) (a) Find the curl of the…

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Q: Question 27 Determine the area bounded by f(x)=x²-x and x-axis. A —-unit² А B unit² Ⓒunit² D unit²

A: A detailed solution is given below.

Q: Evaluating √√9-x² dx using trigonometric substitution will (A) 18 18 [*/2 cos²0d0 0 **/2 B 0 Cab…

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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: A detailed solution is given below

Q: 15+0. The improper integral e* dx is

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Q: Evaluating √√9-x² dx using trigonometric substitution will lead to: 57/2 A 18 "/2 cos²0d0 35*1/2 B…

A: ANS: B

Q: dx Transforming - using miscellaneous substitution will yield to secx + 1 A -dz 1+z² B 1² 2-2z² 1+z²…

A: Given problem:-

Q: Which of the following can be determined given 3 3 [ f(x)dx=5₁ g(x)dx=7, and √ √h(x) dx = -5 3 A √…

A: See the details solution in below

Q: w/N Let f(x)=√√3x-2 on the interval y-axis and find the volume of the resulting solid. Revolve the…

A: Application of integration

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

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Q: 2 Let f(x)=√√3x-2 on the interval y-axis and find the volume of the resulting solid. 43x A -unit3…

A: Let's find volume of solid given curve.

Q: ral: Seln(2x²+3x-4)³ (4x+3)dx

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Q: Find the slope of the line tangent to 2xy + π sin y = 2π through the point (1, π/2).

A: The slope of the line tangent to 2xy+πsin y=2π through the point 1,π2.

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

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Q: X √√/31/22 Solve the integral: 3√/x² A + C 6 B 6√√√x + C C3√√√x² + C C) dx

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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: limit of integration

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

A: The integration are

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

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

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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: Evaluate the improper integral (A) diverges B (Q) Na O ساح 3 1²23 -dx

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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 (e²-1)²…

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Q: Question 9 d If g(x) = ·S*^[e'− In(2t+1)]dt, find g''(x) . dx -2 4 A (2x + 1)2 4 B (2x + 1)²…

A: Using leibnitz rule.

Q: 1 √√√√√x + x S Solve the integral: 5 @ =³√√/1+ x ³²³/ + C A {m/1+x²³² |+c ==ınlı 5 6 B C ©…

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Q: (a) Find the vertex and axis of symmetry of the quadratic functi or concave down. (c) Graph the…

A: we have to vertex and axis of symmetry

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

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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: Find the area bounded by : f(x)=e*, g(x)=e* and x = 3. (A) (e³-1)² e3 sq. units B (e³+ 1)2 e3 (C)…

A: To find the area bounded by curves

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: I the area bounded by : f(x)=e*, g(x) = ex and x=3. -X ) (e²-1)² sq. units e2 (e³ + 1)² e3 (e³-1)²…

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Q: The gradient at any point (x, y) of a curve is given by dy-3x² +ax-36 where a is a constant. The…

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Q: Let f(x)=√√3x-2 on the interval volume of the resulting solid. 43л A -unit 3 125 43л B 135 83ñ 125…

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

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Q: Given √√2/10 dx, determine all value/values of P for which the improp хр onverges? A) {0,1} B)…

A: Topic:- application of integration

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

A: A detailed solution is given below.

Q: dx (x+1) log(x+ ) In[log(x+1)] + og² (x+1) + C

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

Q: Find the area of the region bounded by x²y = 1, y = x and y = 4.

A: To find the area of the region bounded by x2y=1, y=x and x=4.