4. Use the washer method to determine the volume of the solid obtained by the revolving the region bounded by f(x) and g(x) about the x-axis.

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: The general solution of the equation (D4 +D²)y= -12 is A y=c₁ + c₂x + c3cosx + casinx+3x² B y=c₁ +…

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Q: The hyperbolic paraboloid (saddle) f(x, y) = x² - y² + 4 is shown in the 3D model below. Find the…

A: Here, to find the volume f(x,y)=x2-y2+4 between the rectangle R=[-2,4]×[-1,2]

Q: 6. Find the area enclosed by the curve x² + 8y + 16 = 0 the x-axis, the y- axis and the x-4 = 0…

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Q: x³√/x² + 1dx

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Q: The general solution of (D³-5D²-6D)y=0 is Ay=c₁+c₂е¯x + c3e6x By=c₁ex+c₂e²x + c3e³x Ⓒy=c₁+c₂e²x +…

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Q: -X Find the area bounded by : f(x)=e*, g(x) = ex and x=3.

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Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

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

A: Let's find volume of solid when curve rotated about x axis.

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A: Given  v = lnxy + ex+y We have to determine  ∂2v∂x∂y.

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: TL 2 Evaluate the integral: sin(3x)cos(3x)dx 3 1 A B C D H|m 3 16 1 3 16

A: To evaluate the integral. Option c is correct.

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

A: Answer: A

Q: dx Transforming secx + 1 2-2z² A 1+z² ® √ ₁ + 2²/1d² +z² B -dz 1-z² z²+z C / 1-z² Ⓒ / 1-²/²0 D 1+z²…

A: To find the transformation of the integral ∫dxsec x+1 after using miscellaneous substitution.

Q: .b if f is continuous on [a,b], and f(x) 20 then √VF(x) dx = f(x) dx T True F False

A: Topic: application of integration

Q: •+∞0 The improper integral * fe 0 A) 0 B e C (D) 1 ∞ ex dx is

A:

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

A: Given:      fx=x-13       gx=x-1 Volume of solid generated by revolving around the region is…

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

A: On solving this we will get

Q: tanx If f (x) = A (В) (ⒸC) D - St 0 sec 3x 1+ e tanx In (secx) √ 1+tan ²x 1+ e tanx sec²x 1+elanx…

A: Finding the derivative of the integral

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Q: X lim x→1 x-1 Your answer x In x

A: Let's evaluate given function by using l'hospital's rule.

Q: H.W // find the integral _1=√15 e-x³².dx. using 7. dx. using two and three points of Gaussian -1.5…

A: In numerical analysis, the Gaussian Quadrature method approximates the definite integral of a…

Q: What kind of the polar graph has the equation r = 2 + 2 cos 0? limacon cardioid lemniscate…

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Q: To evaluate the integral sin ³0cos (A) sin²0=1-cos²0 1-cos20 B sin ²0 2 sin20 sin cose 2 1+ cos20…

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Q: If y = arcsin (e5e), Check Answer dy da

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Q: Question 31 Evaluate the integral: A B C D H|m 1 1 13 1|6 sin(3x)cos(3x) dx

A: To evaluate the integral.

Q: If (x+1) dx (x+2)(x-1)² 1 93 2 93 S- A B D -io 1 W|N -io 2|3 2|3 9 3 A x+2 + B + x-1 C (x-1)² (x -…

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Q: HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. (D^3 – 2D + 4)y = 0 ; y = –2 , Dy = 8, D^2y = 0, when x =…

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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: Evaluate each of the following line integrals. Sc [(x² - y2)dx + (2xz)dy + (xy-yz)dz] where C: x =…

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

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

A: Using disc method, volume is evaluated.

Q: . The implicit solution for the differential equation y' = x³y is A. In x = y² + c B. 3 lnx = y² + c…

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Q: QI/ sin x a) find dy/dx for the equation (y 1+cos x b) find f'(x) for the equation f(x) = sec x

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

A: To write down the number of antiderivatives a function can have.

Q: Refer to the definite integral to answer the following questions 3 1² (2²) (x²) dx

A:

Q: Use implicit differentiation to determine the derivative of the following functions. 1. 3x²+2y²-81…

A: Given :3x2+2y2-81=05x2+4y=16

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Q: Determine the area bounded by f(x)=x²-x and x-axis. Ⓒ / unit² A ® B / unit² © unit² D -unit²

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

A:

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: Given g is a differentiable function and range of g is on the interval I and  F is antiderivative of…

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. units…

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Q: 3+ Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx (3e)3+ sinh2x A +C 2+In3 (3e)3 + cosh2x +C…

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Q: From a table inside a room with current temperature of 32 degrees Celsius, a left over Fried Chicken…

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Q: 1. The Maximum point of y= 9-x² x²-4

A: This is a problem related to maxima and minima. Based on the general formula and concept we will…

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Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 + C (3e)3+cosh2x B 2ln3…

A: