1/2 Scave [ (a²-x² - x²) ¹²h dx (8) = √5 (9² - x²)³/²2 [³ (a²-x²) ¹1²2 0/² ] + c 15

Q: Set-up the integral using horizontal element for the area of the plane region, 0≤x≤ 2 (플 (-snx) dx…

A:

Q: 3 z²+1 2. Find the area of the region in the first quadrant between the graph of y the z-axis. If…

A:

Q: Set-up the integral using vertical element for the volume of the solid obtained by rotating the…

A:

Q: √√2₁ y = ¹, y-axis, y=1&y=3; OY

A: Volume of solid obtained by revolving region around y axis is evaluated.

Q: TYPEWRITTEN

A:

Q: The area in the first quadrant bounded by y = x², the circle x² + y² = 2, and the x-axis is equal to…

A: We have to find the value of a and b.

Q: ngth of 45 cm. How much work is needed to stretch the spr

A:

Q: The rate of depreciation of a building is given by D'(t) = 2000(10 - t) dollars per year, 0 ≤ t ≤…

A: solution:-(a) according to the given graph the total depreciation of the building over fitst 5 years…

Q: Differentiate f(x) = ln(tan 5x). Use exact values. f'(x) =

A:

Q: 1+x² 1. Find the area of the region bounded by the curve y=- 2x² and the lines y = 0, y = x, x = 2.

A: Given problem:-  1. Find the area of the region bounded by the curve y=(1+x2)/2x2 and the lines y =…

Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

A:

Q: Evaluate the integral: √ S - (9x²+7x) (x−1)(x+1)² dx = ← +C

A: Given; I=∫-9x2+7xx-1x+12dx   As we know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: The graph of y = z² is shown on the grid. Graph y = (x - 3)² – 2. 10+ 9 40 05 15 8 * 50 An NE

A: graph of function

Q: Evaluate the definite integral I. 1 = [₁² [(e-x + 1) dx -1 I =

A:

Q: A+B+C =0

A:

Q: Consider the ODE: (2x siny)dx + (x2² cosy + cosy)dy = 0 a. Solve the ODE by separation of variables…

A: We have to solve ODE by seperation of variable

Q: 6. A curve which intersects some straight line in an infinity of points (but for which not every…

A:

Q: 2 If "IF(x)dx=6 and frox)dx=7.50mm [rodr then f(x) dx = 5

A:

Q: Which of the following functions will involve a factor of t" the t-axis?

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: If w = 2x² - 2y + 3z + sint and x-y=t, find the partial derivatives below. aw a. (3) X.2 c. (H) b.…

A:

Q: 4. Evaluate the following integral using cylindrical coordinates: LI [zd x dz dy dx

A: Let's evaluate given integral by using cylindrical coordinates.

Q: Evaluate the integral S cos ³ x + 8 sin x cos³² x + 6s in ² x dx; cosx #0 2 cos²x

A:

Q: Problem. Suppose you are having a dinner party for a large group of people, and you decide to make 2…

A:

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 4x + 8y = 8,…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y = x + 1, y = 0), and X=2…

A:

Q: the following i -7x²+x-

A:

Q: Find the sum of the geometric series below: 5 5 5 + + 5+ + 3 9 2187 49200 A 6561 5465

A: Topic:- sequence and series

Q: Evaluate the given integral as indicated: Use Integration by Trigonometric Substitution x³ dx 5 (4x²…

A:

Q: 3. Which one of the following statements is CORRECT? A. ff(x) dx + f(x) dx = 0 B. ff(x) dx-f(x) dx =…

A: These statements are related to properties of integration. Here, We will use some integration…

Q: (5) Suppose the population of a certain bacteria in a laboratory sample is 100. If it doubles in…

A:

Q: Evaluate the integral given below. Check your answer by differentiating- NOTE: Enter the exact…

A: To evaluate the integral given below. To check theanswer by differentiating.∫16t-6 et dt=?+C

Q: HICI IL X ot N xu[(x-+)-C

A:

Q: dy dx 4x + y 2x+y

A:

Q: Find all solutions to the given equation. In the choices, k runs through all integers. √3csc(x)+2=0…

A: We can find the answer as below.

Q: 3) Draw the missing figure on the sequence below and provide solution/explanation:

A: Follow the procedure given below.

Q: 6. Set up integrals to compute the arc lengths of the curves y = r², y = 26, y = x¹⁰ defined for z…

A: Let's find arc length of given curves on interval [0,1].

Q: Solve the improper integral and determine if it is convergent and divergent 9 √2 (1-32), dz Oa .…

A:

Q: The numerical value of the lim 818 n+3 nln (2) n+1 is equal to

A: We use L'Hôpital's rule to solve the limit.

Q: Evaluate the following definite integrals Lx finck if fo for if xxO (sin x 1 x >0

A:

Q: Using Rationalizing Substitution S O Arctan(y) + C Ⓒ2Arctan(y) + C O In(y) + C O2ln(y) + C dx X√√x-1…

A: The integral is  ∫ dxxx-1=∫f(y)dy

Q: II. Find dy/dx of the following functions: 4. ytan (tanh.x) 5. y=e³x sechx 6. y = √sech5x

A:

Q: j (4x³+8) dx -1 ) Use the trapezoidal rule to approximate the integral. (4x³ +8) dx~ Round the final…

A:

Q: Evaluate the integral of the following: S(-4t+12) (5t +15)dt

A:

Q: find dy/dx and dy/dx2, if : x = a(cosθ + θsinθ) and  y = a(sinθ - θcosθ)

A:

Q: Assume acceleration due to gravity is -32 ft/s². A ball is thrown vertically upwards from a platform…

A:

Q: y = e√√²t sin√√2t √2 (s-√2)² + √2 A) √2 (s -√2)² + 2 √2 (s + 2)² + 2 B) 2 (s-√2)² + 2 9

A:

Q: √x+1 - dx = y² + 4y+ 4in(y-1) + C, express the final answer in terms of x- √x-1 Using Rationalizing…

A:

Q: Find the critical points of ƒ(x) = −6x² + 4x² − 9 and apply the Second Derivative Test (if possible)…

A: We have to find point of local maximum and local minimum for the given function.

Q: 1. 3x, If R is the region in the first quadrant bounded by x-axis, 3x + y = 6 and y = evaluate ff 3y…

A:

Q: Find the Cartesian form of the equation in spherical coordinates given by p = 2 cos p.

A: We have to solve above question and find cartesian form