= 4 R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

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

A:

Q: 2x ind the derivative of: 2e cos(8x). [Hint: use product rule and chain rule!] se e^x for e*. ow,…

A:

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: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, th (A) 0 and…

A: Topic:- application of integration

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

A:

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

A:

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

A: To find integrand the steps are as follows.

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: In the indefinite Integral Sin(cosh x + ex). integrand? sinh x + ex cosh x + ex dx, what is the

A:

Q: Question 27 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct…

A: A detailed solution is given below.

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

A:

Q: Q/IF 3= sin(X) (²314) y = 3² sin(x) cos(x) Prove that

A: To find y':

Q: e integral: J √√√x+x F1+x X + C 1 x C 5 + C 6in|5+ x² +C 6

A:

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: e the triple integral: (x+y+z)dydxdz 6 24 18 12

A: Topic :- application of integration

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

A: In this question, we want to know the integrand of the given Integral.

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: **/2 Ⓒ 18/¹/2 (A) sin²0d0 0 **/2…

A: See the details solution in below

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

A:

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

A:

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

A:

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

A: To solve the integral.

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

A: Solved below

Q: d²y If x=5+ cos20 and y=3- sin20, what is ? dx² A csc ³20 (в B - cot20 Ⓒ-csc ³20 D cot20

A: Given: x=5+cos2θ and y=3-sin2θ Now, dxdθ=d5+cos2θdθ=-2sin2θ and    dydθ=d3-sin2θdθ=-2cos2θ Now…

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

A:

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

A: Length

Q: S₁² = P² 1 хо A (-∞,1] B {0,1} с (1,00) D (-∞0,00) Given dx, determine all value/values of P for…

A: Here we have to determine all values of p in which the given improper integral is converges.

Q: y'+xy=xy^3 Solve for the solution What is the integrating factor? What is the dependent variable?

A:

Q: What kind of polar graph has the equation r = 3 ? * cardioid lemniscate circle rose petal

A: Solution: equation r=3

Q: Using the method of variation of parameters, the form of a particular solution Yp of…

A: Here, the given DE is: (D2+25)y=4x2-3e5x

Q: Iff and g are continuous on [a,b] and f(x) ≥ g(x) for all x € [a,b] th then A True B False [ f(x)dxz…

A:

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: y = 2 sin 3x 1+3cos2x

A: We can solve this as follows:

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

A: Washer method

Q: Evaluate the triple integral: A) 12 B) 6 C) 24 D) 18 3 2 1 (x+y+z)dydxdz

A: We have to choose correct option

Q: Evaluate each of the following line integrals. cy²sin³x √1+ cos²x ds where C: y = sin x going from…

A:

Q: Evaluate the double integral: A B C D m 100 +10 9|N NIG 4 S** 2ydydx 1

A: A detailed solution is given below.

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

A:

Q: Evaluate the improper integral A 0 B 2 (C) с D) diverges 3 4 12330² dx

A:

Q: Solve the integral: Seln(2x²+3x-4)³ (4x+3) dx (2x²+3x+4)¹4(4) A + C 3 eln(2x²+3x-4)³ B + C…

A:

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 -…

A:

Q: a + bx² 3ax + bx³ dx

A:

Q: A solution of a differential equation free from arbitrary constants obtained from the general…

A: The complete Solution of an Ordinary differential equation is composed of a general solution and a…

Q: The population of a community is known to increase at a rate proportional to the number of people…

A: Let's find  initial population and after 10 year population.

Q: How many antiderivatives does a function of the form f(x)=x" have when n*0? A) none B) 1 infinitely…

A:

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

A: In the given problem we have to find out area of region bounded by given curve with the help of…

Q: Which of the following is NOT a method for finding volume of solids of revolution? A conic method B…

A: