62.
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![SE SECTION 7.2
Trigonometric Integrals
499
61. If " tan°x sec x dx = I, express the value ofvon9
aluate
* tanx secx dx in terms of I.
=b Zn 200 X 2
62. (a) Prove the reduction formula
cos 0 d0 and
9 sin-0
w niz
tan"-2x dx
tan2n-1
| tan2"x dx
2n – 1
Substitution Rule
(b) Use this formula to find tan°x dx.
xb xN 200 X 200
v 63. Find the average value of the function f(x) = sin²x cos'x
on the interval [-Ħ, 7].
- IT,
64. Evaluate sin x cos x dx by four methods:
(a) the substitution u = cos x
the substitution u = sin x
tutisedu2
(c) the identity sin 2x = 2 sin x cos x
10 olonio so d) integration by parts
5Tw Ingoini on
11ebnei- 65-66 Find the area of the region bounded by the given curves.
Explain the different appearances of the answers.
This can
sin-x, y = sin'x, 0<x< T
cot 0 in
y = tan²x, 0 <x< /4
65. y =
66. y = tan x,
md the hypotenus
th 67-68 Use a graph of the integrand to guess the value of theas
2 ol no9wi integral. Then use the methods of this section to prove that your
2 or bae (d guess is correct. nut B
2
aduan slem 67. cos'x dx
68.
sin 27x cos 5Tx dx
Jo
hnbsnd-01so A 3BA SHO O COLU IS vatid even
69-72 Find the yolume obtained by rotating the region bounded](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F075d9603-09c6-4bc2-a245-638144d34596%2F4989dad6-19ea-4ba6-b765-ef54a4e6fc37%2Fvrsgppo_processed.jpeg&w=3840&q=75)
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