Question 3 Iff is continuous on [a,b], then T True F False b then f(x)dx = f(x)dx T a

Q: (x+1)dx (x+2)(x-1)² S A 2 - x+2 B -1 + (x-1)2 ]dx. the values of A & C respectively are:

A: integration

Q: Solve the integral: S- ® in/1+x A) an 1 B_5n/1+x' 5 6 1 √√√x + x + C + C c dx

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)=x²+2x+…

A: The volume of the solid is 63π unit3

Q: d^3-5d+4)y=0 when, x=0, y=-2, dy=9, d^2y=0

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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: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. cos y A =C sin x sinx cosy…

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

A: To find the area bounded by curves

Q: Evaluate: L-¹{. S-2 (s+ 2)² - 49 4 Â) e-2t(cosh7t - -sinh 7t) 4 B e²t(cosh7t + sinh 7t) (C) e2t…

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Q: a + bx² 3ax + bx³ dx

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Q: Let f(x)=√3x-2 the y-axis and find the volume of the resulting solid. 83 (A) -unit ³ 135 83 (B)…

A: We will draw the curve f(x) and y=1. Points of intersectionf(x)=3x-2   and y=11=3x-2 1=3x-2x=1Point…

Q: Solve for the area of the region bounded by x² = 4y + 4 and x = y = 2 (A) none of the choices 128 B…

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Q: Two small planes approach an airport, one flying due west at 100 mi/hr and the other flying due…

A: Solution is here

Q: Evaluating 9-x² dx using trigonometric substitution will lead to: A of th (A) cos²0d0 [*/ cos²0de Ⓒ…

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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: 3. Look at the figure below. Find the value of x and the measure of each angle. n 1.x = 2.42 = 3.26…

A: We know that alternative interior angles are same Therefore 5x-14=3x+18 Subtract 3x+18 from both…

Q: If f(x) = A B D tanx S™ 0 1+tan²x 1+etanx sec ³x l+etanx In (secx)√1+tan²x 1+etanx sec²x tanx 1+12…

A: Using the Leibnitz rule:

Q: If f(x) = A B C D tanx S 0 sec²x √1+1² 1+e¹ -dt, then f'(x) equals 1+e tanx In (secx)√1+tan²x 1+ e…

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and the x-axis.…

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Q: dx xy+3x-y-3 dy xy-2x+4y-8

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Q: Given than f(x) dx = 4 and A None of the given choices ℗ 25 (2) dx = [1 (2) de B f(x) © f (x) dx =…

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x) =…

A: To find the volume of the solid.

Q: Find the area of shaded region. 1/4 sq. unit 1/2 sq. unit T/4 sq. units 1/2 sq. units j r² = sin 20

A: The shaded region is bounded by the polar curve r2=sin2θ in the first quadrant.

Q: An engineer is designing the runway for an airport. Of the planes that will use the airport, the…

A: Given:   To determine: The minimum allowed length for the runway.

Q: O O O O It is reflected over the x-axis and shifted right three units. It is reflected over the…

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Q: The general solution of (D³-4D2)y=0 is A y=c₁+ ₂²x+c₂e-²x By=c₁+ c₂x + c3e4x - 4x Ⓒy=C₁ + c₂x + c3е¯…

A:

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

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x+1. 3 A unit² 3 Ⓒunt² unit² D…

A: topic- area bounded by curves

Q: Question 33 If g(x)=- A) B D d = 2√²-1 (2 ·S^*^[e'-In(21+1)]dt, find g''(x) - 4 (2x+ (2x + 1)² e*…

A: Solved below.

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and…

A: The functions are f(x)=x2+1 and g(x)=-x2+2x+5

Q: 3x+ +4x +4y² = 25x³

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Evaluate the integral: 1 A 6 B С 3 D HIM P 16 sin(3x)cos(3x) dx

A: Solve by integration

Q: Find the volume of the solid of revolution generated when the area described is rotated about the…

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Q: Q/IF 3 = sin(x) 0²³²141 y= (4) y = 3/2 I sin(x) cos(x) Prove that

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Q: 1. f (x² + 1)(x² + 3x) dx

A: To evaluate the given integral.∫x2+1x3+3x4dx

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

A:

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

A: B option is correct.

Q: y = Arctan ( 2+x 1-2x

A: We have to find derivative

Q: (os(t) 2 = Ste S₁ canned with CamScanner cos(+ sin(t)) dt

A: F = 12π∫02πecost·cosπ3+sintdtThis is a complex integrand, hence numerical technique is used. F =…

Q: 1. Find the area between y = - x² + 4x and y = x² - 6x + 5. Graph and shade the area required.

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Q: the indefinite Integral In(cosh x + ex)- A In(cosh x +ex) Sinh x + e* cosh x + ex (В sinh xtex sinh…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and 1 A -unit² 3 B -unit² 3 -unit² 4 1…

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Q: Initially 80 grams of radioactive substance was present. After 4 hours the mass had decreased by 6%.…

A: Let's find amount remaining after 40 hours.

Q: Cx²e*dx

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Q: 1 11 Given 1 [²_f(x) dx = 0 and [ f(x) dx = 1 1 ₁ ¹3f(x) dx - 2f(x)dx. evaluate 6 0 -1 55 A 6 11 B 5…

A: A detailed solution is given below.

Q: A B (C) D dx -2 (2x + 1)² (241) 2 2 (2x + 1)² ex - ln( 2x + 1) 8

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Q: May I ask why there is a plus 8 in the final answer?

A: We have to explain why there is 8 in final answer.

Q: Question 9 Which of the following represents the volume of the solid generated by revolving the…

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Q: 10 Σ (3n – 1): 125 n=1 10 Σ–1 (3) -1, 125 Σ (3n – 4): 125 10 Ο Σ(3n – 4): 125 Ο Ο O e Θ

A: Verify all the option   then find the sum.

Q: 2. Find the area under the curve y = x² from x = 0 to x = 3. -y-x² (1,1) x-1 (3,9) x-3

A: Solved below.

Q: To evaluate the integral sin³0cosº0de by trigonometric transformation, we use the identity; 1- cos20…

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