7. Find the area bounded by the parabolas x² - 4y = = using vertical strip. 0 0 and x² + 2y and x² + 2y - 12 = 0

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: Which integral below gives the volume of the solid of revolution obtained by rotating the bounded…

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Q: Which of the following is a third degree partial differential equation? 3 дz J2z A др (В D др2 дz др…

A: given data  to find the degree of the partial differential equation

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

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

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Q: Evaluate the double integral [[ cos(x + y) dA, where R is the region bounded by the lines y = r and…

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

A: Here we have to find the integral for finding the volume.

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

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

A: Here we have to find the integral

Q: Transforming S Ⓒ √ 2²-22²2 =2 A -dz 1+z² z²+z B -dz 1- © S с © S D N dx using miscellaneous…

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

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Q: tank has pure water flowing into It at 10 L/ min. The contents of the tank are kept thoroughly…

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Q: Question 14 dx Transforming S using miscellaneous substitution will yield to secx + 1 Ⓒ √ 1 + 2 ²2/0…

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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: Determine the area bounded by f(x)=x²-x and x-axis. 1 (A) -unit² B -unit² © == unit² C Ⓒ / / unit² D…

A: To find the area of  the bounded  region.

Q: Find the area bounded by: f(x)=e*, g(x)=e* and x = 3. A (e³-1)2 e3 sq. units (B (e²-1)² e2 (e²+ 1)²…

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

A: The integration are

Q: If f(x) = 2[g (x)]³+7, then what is f'(x)? (A) f'(x)=6g (x) g'(x) (B) f'(x)=6g'(x)…

A: Use the chain rule of differentiation and then solve .   As per the bartleby guidelines I am allowed…

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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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: Evaluate the given definite integral [ 2x³ – 6x² dx, from x = 1 to x = 2 X²

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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: 1 S dx 3 x + x Solve the integral: 5 A + x +C 1+x+c n 1+x+c in 1 B + x + C © 6/5+x²³/+c C ® 1+x+c In…

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

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Q: Evaluating ³√9-x² dx using trigonometric substitution will lead to: 15/2 A cos²0d0 B 18 cos²0d0…

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

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Q: Question 12 We can apply General Power Formula of Integration on which of the following integrals? A…

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Q: y=Arccos (x²)

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Q: 5. (D²+4)y=4 cot 2x

A: We use variation of parameters method to solve the given differential equation.

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

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Q: y= 3 Arcsec 3x

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Q: Determine the general parametric solution of the following unsolved differential equations for the…

A: See the details solution in below

Q: The general solution of (D³+4D)y=0 is Ay=ex(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁ex+c₂e²x +…

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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: 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: Which of the following can be determined given .3 3 3 [ f(x)dx = 5, ³g(x) dx = 7, and g(x) dx = 7,…

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

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Q: etermine the area bounded by f(x)=x²-x and x-axis. 1 A unit² 2 B unit² 1 unit² 1 unit² D

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Q: S Given 1 хр for which the improper integral converges? A {0,1} (B (1,00) C (-∞0,00) D (-∞,1] dx,…

A: The given improper integral is: ∫1∞1xpdx Suppose p=1 then: ∫1∞1xdx=ln x1∞=∞ So, diverges.

Q: Evaluate the triple integral: 3 ₂2 0 (x+y+z)dydxdz

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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: y = x ¹ Arctan 4(x4)

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

A: Our Aim is to evaluate the improper integral given below:-∫0∞e-x dx -(i)

Q: iven ·S. A (-∞0,00) B) {0,1} Ⓒ(1,00) D) (-∞,1] dx, determine all value/values of P for which the…

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

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Q: Question 21 dx Evaluate: S (x+1) log(x+1) (A) In 10 log² (x + 1) + C 2 B In[log(x+1)] +C In 10 C…

A: We need to evaluate integral.

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

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

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Q: If f (x) = A) B (C) D tanx √1+1² 1+e' 0 1+tan²x tanx 1+e sec ³x -dt, then f'(x) equals tanx 1 + e In…

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