-3 -4 1 3 4 6 7 Compute each of the following definite integrals: (a) / s f(x)d.x. 10 (b) / f(x)dx. 10 (c) / (-3ƒ(x)+5) dæ. Show all of your work. 2.

Q: -5t +9 dt VEI Evaluate the definite integral given above. Enter your answer as an exact fraction if…

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Q: r² (x²– 1)(x² + 1) , What is the resulting value of the definite integral dx? х-1 O 33 1 + 4 15 O 31…

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Q: Q.1 Find the integral of f 2 /x+ e* ) dx. - 3

A: We will find the integral as following.

Q: 12x + 18 1. What is the indefinite integral of / :) dx ? x3 + 5x2 + 2x –8

A: 1)

Q: 1. Evaluate the indefinite integral (a) S (e2× +– 3) dx (b) S(4x³ + Vx)dx 2. Find the function f(x)…

A: We will use the formula ∫eax dx= eaxa∫xndx = xn+1n+1∫1xdx = ln(x)   Hence 1) a)  ∫e2x+2x-3dx =…

Q: - 23 L f(2)dx = 11 - 82 and - 23 L g(z)dæ = 30 82 and – 23 h(x)dx = 25 - 82 | what does the…

A: Given ∫-82-23Fxdx=1 -1          ∫-82-23gxdx=30-2          ∫-82-23hxdx=25-3We find…

Q: 4 Suppose | f(x)dx = 6, f(x)dx= 5, and g(x)dx = 8. Evaluate the following integrals. g(x)dx = 7…

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Q: Q3: Find the integral for the following functions: - 6 dx 1) 2 x+2

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Q: +-/1 points My Notes 1 BerrApCalc7 5.6.001 1 un du = -un 1C (n n+1 -1).] (Use C for the constant of…

A: Let I be the given integral and say it is A.

Q: Q.1- Evaluate the following integrals (answer two only) a -1° V√x - √x₁ dx 0

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Q: 32. Find the integral: dx k² +1 (-1)*2 (k² +1) а. +C 5(-1)*2*k k? +1 k+1 b. +C (-1)*2* '(k +1)(k²…

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Q: -3 2e4 Evaluate the given integral: Jo 1+e2x dx.

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Q: B. Evaluate the following integrals: x-9 1) S- dx x2+3x-10

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Q: ∫(−6x6−2x3−4)dx

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Q: - 19 f(x+1)-(x2 - 6x +13) Ax + B √x²+bx+c² dx? (3)-In/x² - 6x + 13| + C The integral What is the…

A: Using partial fraction…

Q: If f(1) = 14, f ' is continuous, and integral of 3 1 f(x) dx =17 what is the value of f(3)? f(3)

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Q: L d 1² (²5 2 sin(x) 10 - x dx. to approximate the integral • h 0 =0 • Xo f(x) = • f(xo+h) = • f(xo +…

A: Trapezoidal rule, evaluation of the definite Integral. Given that  ∫252 sin x10-x dx

Q: 4. If the integral value of | f (x)dx = 4 and | f(x)dx =-3 then the value of | f(x)dx is -1 -2 а. —3…

A: It is given that  ∫-14fxdx=4∫-24fxdx=-3

Q: Q3: Find the integral for the following functions: - 2) ſ e3se c(x), sec(x). tan(x) dx

A:

Q: 3 -1 -2 -3 -4 1 2 3 4 5 6 7 8 9 10 Compute each of the following definite integrals: (a) f(#)dr. 10…

A: Given

Q: Calculate the definite integrals (a) I₁ =¹7 (2x − 1)(x + 2) dx - 18 (b) I₂ =2₂¹8 (x + 2)(√√x - 2) dx

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Q: 1. Kgothatso showed her classmates that dx%3D (x- 1) Without showing Kgothatso how you would…

A: 1.AgreeGiven Integral can be evaluated with the formula :∫yndy =yn+1n+1here y =x-1 , n=-23

Q: Evaluate the following integrals. (a) ∫ x3 ex2 dx (b) Find the values of a and b for the curve…

A: (a) Consider the integral: I=∫x3ex2dx……1

Q: 5x+1 What is f'(x) given the integral function f(x) = S cos(e") du?

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Q: x" e ax n-1 ax dx e ax dx Use one of the reduction formulas shown to the right (which are valid for…

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Q: If what does the following integral equal? - 14 73 [6f(x) + 3g(x) - h(x)]dx = - 14 f(x) dx = 11 and…

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Q: 9. Evaluate the following integrals: (Simplify your answers) (a.) [x¹² cos(x-6)]. X+3 8(x-4)dx -2x…

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Q: f(x) = f ¹n (x X dx a = 2, b=4

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: 2e Consider the indefinite integral dx: (e2z + 3)* This can be transformed into a basic integral by…

A: Given,

Q: 1. Evaluate the following integrals. Show all steps! 2 x + 3 dx x(x – 3) 1? — 4x + 6 - dx (b) | (x –…

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Q: Evaluate the definite integral (За3 — 5а + 2) da fo 5а + 2) dx — a) Find an anti-derivative +C b)…

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Q: Given: ((x)dx Evaluate f(v2). There is a function f(x) such that when u = -x³, the resulting…

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Q: Given the function graphed below, evaluate the definite integrals. 4+ 3 2 1 -1 7 -1 -2 -3 -4 1 S.³…

A: Need to find out the definite integrals.

Q: -5e 1 Evaluate the integral: dx. 1 x A. - - 1 5e B. 1+ In 5 C. 0 D.00

A: We have to evaluate to integrate

Q: 0. Let f(2) ) = x + d 1 dx for 1 < x, such that f(1) = 1. Find the general solution. a.

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Q: 4 7 7 Suppose f(x)dx = 5, f(x)dx = - 8, and g(x)dx = 7. Evaluate the following integrals. 2 2 2…

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Q: Given the function graphed below, evaluate the definite integrals. 2 3 4 5 6 7 8 -3 -5 [²ƒ(z)dz = −5…

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Q: 1/4 we use the substitution u = (x²+1)² on the definite integral (x³+x)(x²+1)23 dx then the integral…

A: From the given problem: I=∫01x3+xx2+123dx...1 Let, u=x2+12 Now differentiate with respect to x on…

Q: 1. Find the following definite integrals: 1 (a) / 3r*(3x* – 2)5 dæ 1 r2 (b) - 2² – 1 xe dx

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Q: 6 6 iwen ["r*dz = 320, x³ dx x dx 16, dx = 4, evaluate the following using properties of definite…

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Q: 13. Evaluate the definite integral. 1 а. x6 b. (4x – 1)²dx = С. 7 du = Vu n. d. 2 e. (13 – t3). dt…

A: Here we have to evaluate the given definite integral.

Q: S- 1 x > 2 2x+6 for x < 2 | f(x) = 2 cos (Tx) for Evaluate the definite integral. f (x) d æ = 1…

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Q: a) Find the definite integrals of the following functions (i) Sx(x² +9)10 dx (ii) xp xu)x (iii) S…

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Q: (2) Solve the following. B (a) Evaluate the integral F. dr where F = i³ – y cos x, 3xy? – sin x) and…

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Q: Evaluate the definite integral. *2 e 1/x* dx J1 +s

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Q: 3 Suppose that f(x) dx = 7, | f(x) dx = 5, and | f(x) dx = 10. %3D Evaluate the following definite…

A: (a) The given integral is: I=∫35f(x)dx As we know from the integral theorem,…

Q: C. Evaluate the definite integrals ( show your solutions) 1. S, (x³ – 6x² + 2x)dx - TT 2. 3 cos3…

A: The given questions can be done as follow:

Q: 2.2 Find the indefinite integral of the following: I = S(4x² + 5x – 7)dx а. | b. I = S Vx dx I = J…

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Q: = "+1 + C. 2. The power rule for integrals is x" dx a. Evaluate f da = fx2dx. n+1* 1 b. What goes…

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.