In pair, study and find the integral of the following functions. You will be awarded marks for each problem solved. 14 √(x+5)(x+2) dr. Sez e sin x dx 3. 5x - 2 Ta dx. x²e-3x dx (x + 3)² 4. 1. 2.

Q: The graph C of the equation y = gives the course taken by an oil tanker after leaving port, which is…

A: Here we have to find the arc length.

Q: (D² + 3D + 2)y= sin ex

A: The given differential equation is  (D2+3D+2)y=sinex

Q: (1) Which is the correct formula for finding the derivative of the product of two functions? (fg)' =…

A: 1.the formula of derivative of two function is fg'=fg'+gf'

Q: Q2:Expand using Maclourin series (1 - x 1-x² 2 ln(1 + x4) )? -

A: As per our guideline we are supposed to answer only one question of  multiple type of questions.…

Q: Find the line integrals of F = 4yi + xj + zk from (0,0,0) to (1,1,1) over each of the following…

A:

Q: Find the antiderivative F(x) of f(x) = 8(sec x)(sec x – 4 tan x).

A:

Q: Find the area of the region bounded by y²-x=0 and y²+x=2₁

A: Find the area of the region bounded by y^-x=0 and y^+x=2

Q: What is the particular solution of the differential equation (x+y) dx + (x - y) dy = 0 when x = 0…

A:

Q: 3. Find the area of the region enclosed by the two curves y = x² and y = -2x² + 3x.

A:

Q: Q2: A. Determine if p = ï-3k and q = 61 - 3j-4k are parallel, orthogonal or neither. B. Find the…

A:

Q: Q1: Find the for the following functions: dy dx 1- y = e(x+In 5x) 2- y = cosh-¹ sin 2x 3- y = xsinh…

A: 1)y=ex+ln(5x) 2)y=cosh-1sin2x 3)y=xsinhx

Q: Problem r7 ¯7² xVx² - xVx² 0 + 1 dx

A: Topic:- application of integration

Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

A: The objective is to find the appropriate integral to be used to find the volume.

Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: The path of a satellite orbiting the earth causes it to pass directly over two tracking stations…

A:

Q: (d) Given r(t) = (ln(t+1), t cos 2t, 2¹). (i) Find r'(t). (ii) Find parametric equations for the…

A:

Q: Determine the angles made by the vector V-(-19)i + (-41) with the positive x- and y-axes. Write the…

A:

Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

A: Given problem:- The region in the first quadrant bounded by the graph of y = 8 - x3/2 , the x-axis,…

Q: Rewrite the Cartesian equation r(0) = Enter theta for if needed. = 3 as a polar equation.

A: Topic = Geometry

Q: In the quadratic equation Ax² +BX+C =0, describe the roots when B²-4AC is zero. A The roots are…

A:

Q: 6. y = x Arccsc (¹)

A: we can find the y' as below

Q: Given: ·S- takes the form 20 A 3 8x+1 dx. If we let the substitution =√√4x-5, the final answer 4x-3…

A: Integration

Q: Used Cramer's Rule to find the value of the variables (X,Y,Z) in the following equations x + 2y + 3z…

A:

Q: (-2xy) dx + (Sing-x)dy 3 7 dy + 3xy dx = x ēdx • (3x-2y + 2) dx + (3y-2x-2) dy zo (y + x² ) dx = xdy

A:

Q: Find the transition points. f(x) = x(11-x)1/3 (Use symbolic notation and fractions where needed.…

A:

Q: 9. A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 4√108…

A:

Q: 90 y 2 1980

A:

Q: 4. f²₁(x² x)dx 5. (4- x²) dx

A: topic- definite integral

Q: 2. Evaluate the integral. Do not use hyperbolic functions as the final answer. 1 =dx 2 √3x² - 4…

A:

Q: 01: A. Find the general solution of the following Initial Value Problem (IVP): y+9y-10y = -40t²-72t…

A:

Q: B. Find the general solution of the following 2nd order differential equation: y*+2y+2y=0

A: The given second order homogeneous differential equation is: y''+2y'+2y=0 Therefore, the auxiliary…

Q: Let F(x) = f(x¹) and G(x) = (f(x))¹. You also know that a = Then F'(a) = = 12, f(a) = 3, f'(a) = 4,…

A: Fx=fx4 and Gx=fx4a3=12, f(a)=3, f'(a)=4, f'a4=7

Q: y" + y = secx tanx

A:

Q: (c) Show that the function is a solution of the differential equation (−1)" x2n f(x) = Σ (2n)! n=0…

A:

Q: the appropriate integral to be used to find the volume of the solid generated? 8 7 6 5 4 3 2 1 -1 O…

A:

Q: Consider the function f(x) = 4xe-x². Identify the locations where f has transition points. (Give…

A:

Q: Consider the function f(x) = 4x² Identify the locations where f has transition points. (Give your…

A:

Q: up 1. √ √2x + 1 dx

A: We have to find the solution  As per guideline we have to solve one question please repost other…

Q: f' (æ) =Vx+, f(0)=2 f"(x) = 3x² 16x + 16, f'(0) = 1, ƒ(0)

A: Topic:- application of integration

Q: Using integrals, find the area bounded by the following:  f(x) = 4x2 + 20 g(x) = 8x + 32 x = - 4…

A:

Q: Question 16 The area bounded by y=1-x²₁x+y=1 and the x-axis is submerged vertically in the water…

A: We need to choose correct option.

Q: Find the Differential equation Ⓒ (y + x²) dx = x dy

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: A 60-m climbing rope is hanging over the side of a tall cliff. How much work is performed in pulling…

A:

Q: HOMEWORK 16: Graph the following equations. 6. r = sin + 2cos² 0 7. r² = sin 20 - 3cos

A: we have to graph the given polar coordinates. let r is on x axis and theta on y axis.

Q: s={ 3112 4'2'3'9' =(5, 5.5, 6, 6.5, 7, 7.5,...} = {√2,2√2,3√2, 4√2,...} ={√2,2,2√2,4,...}

A: Topic:- sequence and series

Q: dy Q1: Find the for the following functions: dx 1- y = e(x+ln 5x) 2- y cosh-¹ sin 2x -1 3- y = asinh…

A:

Q: FCILICI. B. Find the general solution of the following 2nd order differential equation: y +2y + 2y =…

A:

Q: B. Find the general solution of the following 2nd order differential equation: y +2y + 2y = 0

A:

Q: Find the lower sum for f(x) = +4 on the interval [-4, 0] using 2 rectangles. 10 "F Submit your…

A: Here we have to find the left sum of given function.

Q: Derive the following function 8. y = tanh-1(sinx)

A: We have to find  the derivative