Subject: Integral

Q: 5) (2,0°) -3 (4) 7) 4 ---22 -1 2 + 21 -1 D | x

A: We know that if r, θ is the polar coordinates then the rectangular coordinates is r cos θ, r sin θ.

Q: Use substitution to find the indefinite integral. Spip +31' ep Spip +31% op

A:

Q: Determine the center of mass for the region bounded by the following. Answer as a fraction…

A:

Q: find the derivatives: 1. y= (tan x)/ (1 + tan x)

A: Solution: 1. y= (tan x)/ (1 + tan x) y'=ddxtan x1+tan x

Q: Consider the curve defined by the equation y = 5x + 3x. Set up an integral that represents the…

A:

Q: ecosh z √x+1 Let F(x) S 1. Find F(0). 2. Find F'(x). sin(1 t) dt.

A: Let's find value of given function.

Q: Let L(c) be the length of the parabola f(x)=x² from x = 0 to x=c, where c20 is a constant. a. Find…

A:

Q: Solve the system of differential equations. = - X1 6x1 + 2x2 X2' - 2x1 - 10x2 2, x₂(0) - 22 = x1 (0)…

A:

Q: Find the area of plane region bounded by the curves y = x³, y = tan² z - 3 and the inequality 0≤x≤

A: To find the area of plane region bounded by the curves y=x3, y=tan2 x-3 and the inequality 0≤x≤π2.

Q: Solve the following problems showing detailed solutions. Draw the complete figures for each…

A:

Q: Evaluate the integral. 34 1 8- dx

A:

Q: The entire graph of the function g is shown in the figure below. Write the domain and range of g as…

A: Find the domain and range

Q: Use substitution to find the indefinite integral. X 1²2* S= 4x² +2 X 4x + 2

A:

Q: 13. Given the triangle below, find the value of c to the nearest tenth. side c = units 33 b 3.4…

A: Explained below

Q: If the sides of an equilateral triangle are increasing at a rate of 6 m/min. How fast is the area of…

A:

Q: If there is no solution, state that there is no solution and explain why.

A:

Q: Approximate the sum of the series by using the first six terms. (See Example 4. Round your answer to…

A:

Q: Given cost and revenue functions and C(q) = 115q + 31000 and R(q) = -3q² +2500q, how many items must…

A: Let's find how many items must be the company produce and sell to break down.

Q: Using Wallis formula, find the integral of the expression. Answer in fraction form, no units, no…

A: We have to find out the integral

Q: Evaluate f , rydyda Select one: a. 3 b. 1 C. 2 d. o

A:

Q: Evaluate the geometric series or state that it diverges. 7² 7³ 12 12² Select the correct choice…

A: We have to find out the series sum

Q: Assume that x² + y² = 4xy. Then y' Select one: True False 2x-4 4+3y²*

A: Let's solve derivative of function  and maximum value of given function.

Q: f sin x ln(cos x) dx

A:

Q: ) Find dw if w = xe³/², x = t², y = 1 — t, and z = dt 1 + 2t.

A: Topic:- application of derivatives

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A:

Q: lim ∞ + X 3x² + 2x - 1 3√7+4x+x² + 3x

A:

Q: Find the differential dy of the given function. y = √√√√9-x²

A: Given y=9-x2 we need to find dy

Q: Evaluate cos(x) - 1| dr.

A:

Q: Given f(x) find f'(x) f'(x) = 2 ¹(√2 x² + 3 In =

A:

Q: 7. Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3. Then the area…

A: Given

Q: Evaluate the integral: fe* sinhxdx. Select one: O a. -+C 0b. ²+0 ++ C d+C

A: We can solve this as follows:

Q: Using Cramer's rule to solve the following system of equations, what D, D, D and D₂? are 4x + 3y +…

A:

Q: 2 and x = 6. 4. Find the area bounded by the parabola y² = 4x and the line y = 2x - 4. ² and Find…

A: To find the area of region enclosed by given curves.

Q: If y = 1 and 2 = 1, find Select one: a. -1 O b. -t O c. 1 O d. t

A:

Q: The two-dimensional Laplace equation, f(x,y)=-4x+2y-7 Find 2x² 22²4 for the given function. 2²1 2²²…

A: Given function f(x,y)=-4x+2y-7

Q: The function fis defined as f(x) = -7 3x²+2 Find f(x-5). Write your answer without parentheses, and…

A:

Q: recurrence relation for the sequence {dn} that gives the amount of drug in the blood after the nth…

A:

Q: Find the area of the region bounded by the graphs of the equations. y = 1+√√x, x=0, x= 8, y = 0…

A:

Q: 21 21 The two-dimensional Laplace equation = 0 describes the potentials and steady-state temperature…

A:

Q: 1.find the derivative of In[In(Inx)] 2. find the derivative of e(2x+Inx

A: Using chain rule of differentiation.

Q: Determine whether Rolle's Theorem can be applied to fon the closed interval [a, b). (Select all that…

A:

Q: Find the volume of the described solid of revolution or state that it does not exist. 1 The region…

A:

Q: Evaluate the following integral. Assume a and b are real numbers and n is an integer. Sx(ax + b) dx;…

A: By considering u=ax+b we can integrate it.

Q: Use the method of cylinders to determine the volume of the solid obtained by rotating the region…

A: answer is in next step . please give a like

Q: If y=u³ and u = 4x² - 2x + 5, give dy dx

A:

Q: Find a formula for the sum of n terms. Use the formula to find the limit as n - ... -(1-1)² T Submit…

A:

Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…

Q: Let f(x) = ln(x7) f'(x) = ƒ' (e²) =

A:

Q: What is the allowable error in measuring the edge of the cube that is intended to hold 8 cu.m. if…

A: Given problem:- What is the allowable error in measuring the edge of the cube that is intended. to…

Q: Find the volume of the solid under the surface z = × siny that lies above the rectangle R = [0,1] x…

A: