Evaluate each of the following line integrals. cy²sin³x √1+ cos²x ds where C: y = sin x going from (0,0) to (,1).

Q: Find the length of the curve of 8x = y² + 2y-² from y = 1 to y = 2.

A: Length

Q: Problem Solving: Prob. 1 A block of mass M = 10 kg is sitting on a surface inclined at angle 0 =…

A: Given that M= 10 kg and coefficient of static friction = 0.5 1. Minimum force necessary to prevent…

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

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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: 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: X √√//dx Solve the integral: A √x 3 B 3√√√x² +C Ⓒ6√√x +C 3√√x² D + C 6

A:

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ unit² ® -unit² Ⓒ unit² 3…

A:

Q: How many antiderivatives does a function of the form f(x) = x^ have when n* 0₂ none 1 infinitely…

A:

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

A:

Q: dx using miscellaneous substitution will yield to secx + 1 Transforming 1+z² Ⓒ √ 1 + 2/²/d= (A) -dz…

A: First of all, note that sec x=tan2x2+11-tan2x2⇒sec x+1=tan2x2+11-tan2x2+1⇒sec…

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

A: D is correct option.

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

A: See the details solution in below

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…

A: We know eln(x) =x

Q: Use the formula for the sum of the first n terms of a geometric sequence to find the sum of the…

A: Given that the geometric sequence is 7,14,28,56,112,....

Q: Question 20 Determine the area bounded by the functions f(x) = (x + 1)³ and A unit² А 3 Ⓒunt² B 3 C…

A:

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: In this question, we want to know the limits of the Integral as a horizontal element.

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

A:

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: Which of these expressions represents the area between the curves y = x^2 and y = 6 - x from X = 0…

A:

Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: A detailed solution is given below.

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

A:

Q: If f(x) = f = Stanu √I+1² 0 1+e' In (secx)√1+tan²x (A) tanx 1+e sec ³x В) Ⓒ (D) tanx 1+tan²x 1+e…

A: Application of integration

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: S dx secx + 1 Transforming Ⓒ / + A -dz 1+z² 2-2z² (B) 1+z² C 12²+2 dz Ⓒ √ 1+2²2 dz D 1-z² -dz using…

A:

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

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

A: The given expression is:…

Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

A:

Q: dy Classify the DE: xdx +xy= A) Separable and Linear (B) Separable but not Linear Linear but not…

A: Given differential equation is

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

A:

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

A: On solving this we will get

Q: Practical Question: An object is moving horizontally with the speed of 50 m/s. When the object at…

A: Projectile motion is the motion of an object projected horizontally into the air and moving…

Q: Find the are bounded by the curve y = x and y = x^2 - 2. * 2/9 sq unit 9/2 sq. units 16/3 sq. units…

A: Use the intersection of the curve and then integrate the upper curve minuses the lower curve to find…

Q: Transforming dx using miscellaneous substitution will yield to secx + 1

A:

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

A:

Q: If a horizontal element is used to find the area bounded by y=√√√x, x=4 and the x-axis, the limits…

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

A:

Q: wen 1₁² / 0x хо A) (-∞0,00) B (1,00) C{0,1} D) (-∞,1] -dx, determine all value/values of P for which…

A: Here  , we have two cases when p=1 and when p not equal to 1.

Q: In the indefinite Integral fin(cosh x + e*). sinh x tex cosh x + ex B) In(cosh x + e*) In(cosh x +…

A:

Q: (A) B (C) (D) **/2 18 [*/ ces **/2 cos²0d0 18 sin²0d0 cos²0d0 0 of the 0 **/2 $ cos²0d0

A:

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

A:

Q: Find the average value of f over region D. f(x, y) = 3x sin(y), D is enclosed by the curves y = 0, y…

A: Here, the domain D is the area enclosed by the curves y=0, y=x2 & x=7 is: A=∫07∫0x2dy…

Q: Əz 5. Givenz = y -4x ?х 6. Find of z = In(xy) a²z 7.Find of z= x³ + 5x²y + 6 əxəy Find дz

A:

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

A:

Q: In the indefinite Integral in(cosh x + e*). sinh x + ex cosh x + ex dx, what is the integrand?

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Q: The expanded form of the differential operator D(xD-1) is A XD²+1 B XD² C XD²-1 (D) XD²-D

A:

Q: The function is x z = y² What is 8²% dy² 2/21/23

A: Let's find second partial derivative of given function.

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

A:

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

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

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

A: Now,The graph of the area bounded by f(x)=ex, g(x)=e-x and x=3 is shown below: