a) state the number of the integral in the attached Table; b) state the values of the constant(s); C) plug in the values of the constants to find the integral; d) simplify. 1.118Basic Integration FormulasSubstitution Formulas1.x+1+C1.5.= np unn+ 1+ C%3Dn + 11.xp uXxpIn |x| + C6.u-1 du =%3D%3D2.xp%3D%3Dnp1.= xp xpaa.3.ex dx = ex + C4.7.e" du = e" + C%3DIntegration by Parts Formula8.ap nnp aan =A Short Table of IntegralsForms Involving ax + b:9.xp.a.In Jax + b| + C%3D10.1.+ C%3Dxp1.bcIn |cx + d| – ° n|ax + b1) + c11.%3D(ax + b)(cx + d)-= xp12.1.xpxv)x+ CIn2ax - 4bForms Involving vax + b:13.%3D= xp3a?9 + xxxq^ – 9 + xvXq +9 + xxx14.1.= xp(0 < 4)이 -Vr? ± a² ± In |x + Vx? ± a² | + CForms Involving x- a?and a?1.xp1.a²15.+ C16.In+ C%3D%3D-a.Forms Involving yx + a²:17.%3D1.dx = In |x + Vx² ± a² | + C18.%3D+ a?Forms Involving Va² ± x²:dx = Va? ± x² – a lna + Va? ± x?+ C19.|%3DU-- = Xp:a.a + ya² ± x²+ C20.1.%3Dxva? ± x?Forms Involving e axand In r:1.= xp mduX| (In x)" dx = x(ln x)" – n | (In x)"-1 dx21.x"-leax dx%3D1.x"+1 ln x1.+1+C(n + -1)23.x" ln x dx =%3D+ u) _See also page 604.(n + 1)²Trigonometric Formulassin x dx = -cos x + Csec? x dx= tan x + Csec x tan x dx sec x + Ccos x dx == sin x + Ccsc? x dx = - cot x + CCsc x cot x dx = - csc x + C -dp-(2x+3)(1-x)1.a) Integral Number in the attached Table:b) Values of the constants: a =b =;%3Dc) Plug in the constants to find the integral (show how you plugged in!):d) Simplify your answer in part c):

Answered: Image /qna-images/answer/819a0612-2b65-45f5-8f73-c8228a4dd5c9.jpg

dx (2x + 3)(1–x) 1. a) Integral Number in the attached Table: b) Values of the constants: a = b = c) Plug in the constants to find the integral (show how you plugged in!): d) Simplify your answer in part c):

dx (2x + 3)(1–x) 1. a) Integral Number in the attached Table: b) Values of the constants: a = b = c) Plug in the constants to find the integral (show how you plugged in!): d) Simplify your answer in part c):

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.3: Quadratic Equations

Problem 53E

See similar textbooks

Related questions

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

Q: Use geometry and properties of integrals to evaluate the followingdefinite integrals.

A: Complete the square: (8x-x2) = -(x2-8x+16-16) => (8x-x2) = -(x-4)2 + 16 Substitute this in…

Q: Noting the range of the integral, compute .2 Jo (2² + 9)2dx.

A: By using inequality of integration

Q: To evaluate the integral 23 V2-2x 3 da, using trigonometric substitution, which substitution should…

A: Given, ∫x3x2-2x-3dx Find which trigonometric substitution is used to evaluate the above given…

Q: Evaluate the integral using NOTE: Enter the exact answer. sec(7x) tan (7x) dx = appropriate…

Q: Evaluate the integral by completing the square and using trigonometric substitution.

A: Integrals and derivatives are considered to be reverses of each other. For example if we have a…

Q: Evaluate the integrals in Exercises using integration by parts

A: Solution of the given integrations can be found with the help of the integration formulas and…

Q: Evaluate the indefinite integral. S csc² 3x v4cot3x – 5dx ,and • Identify what is the u=? and du=?…

A: Given: Intergral is given

Q: Evaluate the integral. "T/3 8 sec 0 tan 8 de IT/4

Q: | VE (2 - 2)* dz

Q: 2. (a) Use substitution to find indefinite integral. (b) /2re xP i+?

A: Since you have asked multiple questions in single request so we will be answering only first…

Q: hello! can you help me with this calculus problem?

Q: find the integral: 1/(x2(4-x2)1/2 using trig substitution that is 1 in the numerator with x…

Q: Evaluate the definite integral by expressing it in terms of u and evaluating the resulting integral…

A: Substitute u = 4x, Differentiate the above, du = 4dx dx=(du)/4

Q: Use the idea from the integral test to find constants A, B such that Asi+ 1 SB 2021 1/3

A: Note that the function f(x)=1x is monotonically decreasing function for x∈[ 1, ∞). Let n∈ℕ, then,…

Q: (z+ 3)° dz (40 – 6z – 22)

Q: Evaluate the integral. 13 dr Vz x²V? – 1 NOTE: Enter the eract, fully simplified answer.

A: Given; I=∫2213dxx2x2-1 ...1 Use the trigonometric substitution to solve the given integral. Let,…

Q: V9x2 + 25 1. х2

Q: [25/² – 36 dz Evaluate the integral: (A) Which trig substitution is correct for this intearal?

Q: Graph the integrand and use geometry to evaluate the integral. jua 8x dx А. 48 О В. 144 OC. 288 O D.…

A: The graph of the integrand is drawn in black colour in below graph, and the red region indicates the…

Q: Evaluate the integral * (2* – 4)" de by making the substitution u a6 – 4. - + C

A: We know that ∫xndx=xn+1n+1+C We make the substitution u=x6-4du=6x5dxdu6=x5dx

Q: Evaluate the integral. NOTE: Enter the exact answer. 1 29 VT dx = 17c +C

Q: Use the substitution x = 8 tan(0) to evaluate the indefinite integral 16dx 22Vx2 + 64 + C EGO LEGO…

A: We are given the integral ∫16 dxx2x2+64. We have to evaluate the integral using the substitution, x…

Q: 16j Use integral tables to evaluate, 3

A: I=32∫ 1x9x2-1 dxu=9x2-1du=18x29x2-1dxdx9x2-1=du9xHence;I=32∫ 1xdu9xx2=u2+19I=16 ∫ 9 duu2+1

Q: Evaluate the integral. (* + 4)3 dx 2145 99 O 2401. O 2145

Q: evaluate the integral by completing the square and using trigonometric substitution.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. (15x – 14)°…

Q: Evaluate the integral. 3x/4 csc e cot e de a/4

A: Given that integration of (π/4 to 3π/4) csc(theta)cot(theta). We know that csc(theta) =…

Q: Evaluate the integral by completing the square and applying appropriate formulas from geometry.…

Q: rIn 2 6. dr 0,

Q: 8. State why the following integrals are improper, then evaluate each integral and state whether it…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. |(142 – 13)*…

A: We have to integrate the given problem by appropriate substitution.

Q: Evaluate the integral (Trigonometric Substitution) 1 (n²z6 – z®)ždz

Q: -1 sec vo) do

A: We will use substitute method to solve the integral.

Q: Use the substitution formula to evaluate the integral. , π/2 20) cot x csco x dx T/6

A: on solving this we get

Q: Use properties of the integral and the formulas in the summary to calculate the integrals.

Q: Evaluate the integral sec 0 tan e de. Answer:

Q: The triple integral ¹²-x² √4x²-y x dzdydx is equal to 0.33 0.08 None of them O

A: Let's evaluate given triple integral.

Q: S(2 + vx)³ Vxdx

A: See the details solution in below

Q: Evaluate the integral (7 – 2x) dæ by interpreting it in terms of area. Answer:

Q: Evaluate the integral. 7/3 sec (0) de

Q: 55. Prove the formula SuT-zidx=;sin using geometry by interpreting the integral as the area of part…

A: We have given the integral;

Q: Evaluate the integral 12 cosh 2r dr.

Q: Evaluate the integral by completing the square and applying appropriate formulas from geometry.…

A: Topic = Integration

Q: Evaluate the integral using FTC I.

Q: Evaluate the integral * -In2 2e0 cosh 0 do -In4

Q: Evaluate the integral. 17xe dx +C %3D ENOTE: Enter the exact answer.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. J tan6(9x)…

A: The objective of the question is evaluate the indefinite integral with substitution method.

Q: 4) Show that the circumference of the unit circle is equal to 1 1 dæ (an improper integral) x2…

Q: Evaluate the integral |-1|2 – 4z| de

Question

a) state the number of the integral in the attached Table; b) state the values of the constant(s); C) plug in the values of the constants to find the integral; d) simplify.

1.
118
Basic Integration Formulas
Substitution Formulas
1.
x+1+C
1.
5.
= np un
n+ 1
+ C
%3D
n + 1
1.
xp uX
xp
In |x| + C
6.
u-1 du =
%3D
%3D
2.
xp
%3D
%3D
np
1.
= xp xpa
a.
3.
ex dx = ex + C
4.
7.
e" du = e" + C
%3D
Integration by Parts Formula
8.
ap n
np a
an =
A Short Table of Integrals
Forms Involving ax + b:
9.
xp.
a.
In Jax + b| + C
%3D
10.
1.
+ C
%3D
xp
1.
bc
In |cx + d| – ° n|ax + b1) + c
11.
%3D
(ax + b)(cx + d)
-
= xp
12.
1.
xp
xv)x
+ C
In
2ax - 4b
Forms Involving vax + b:
13.
%3D
= xp
3a?
9 + xxx
q^ – 9 + xvX
q +9 + xxx
14.
1.
= xp
(0 < 4)
이 -
Vr? ± a² ± In |x + Vx? ± a² | + C
Forms Involving x- a?
and a?
1.
xp
1.
a²
15.
+ C
16.
In
+ C
%3D
%3D
-
a.
Forms Involving yx + a²:
17.
%3D
1.
dx = In |x + Vx² ± a² | + C
18.
%3D
+ a?
Forms Involving Va² ± x²:
dx = Va? ± x² – a ln
a + Va? ± x?
+ C
19.
|
%3D
U-- = Xp:
a.
a + ya² ± x²
+ C
20.
1.
%3D
xva? ± x?
Forms Involving e ax
and In r:
1.
= xp mduX
| (In x)" dx = x(ln x)" – n | (In x)"-1 dx
21.
x"-leax dx
%3D
1.
x"+1 ln x
1.
+1+C
(n + -1)
23.
x" ln x dx =
%3D
+ u) _
See also page 604.
(n + 1)²
Trigonometric Formulas
sin x dx = -cos x + C
sec? x dx
= tan x + C
sec x tan x dx sec x + C
cos x dx =
= sin x + C
csc? x dx = - cot x + C
Csc x cot x dx = - csc x + C

-dp-
(2x+3)(1-x)
1.
a) Integral Number in the attached Table:
b) Values of the constants: a =
b =
;%3D
c) Plug in the constants to find the integral (show how you plugged in!):
d) Simplify your answer in part c):

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution