Integral of sine squared X

Integral of sine squared X:

1) Integrate the function f(x) = 4sin 3x.

2) Integrate the function f(x) = sin (3x + 11).

3) Integrate the function f(x) = sin 3x + 3x²

Solutions:

1) - cos 3x + C

2) - cos (3x + 11) + C

3) - cos 3x + + C

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Graphing equations

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How to calculate Ratios

Functions

Increasing and decreasing functions:

Extreme values calculus is defined by Fermat's theorem, which states that they must occur at critical points.

If f(x) has an extremum on an open interval, then the extreme value occurs at a critical point of f(x).

If f(x) has an extremum on a closed interval, then the extreme value occurs either at a critical point or at an endpoint.

Critical points of f(x) are defined as the values of x* for which either f'(x*) = 0 or f’(x*) does not exist.

One can distinguish whether an extremum is a local maximum or local minimum by using the first derivative test or second derivative test.

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Meters to centimeters

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Algebra questions and answers

F x Maths

F x Maths

A ) V only
B ) I and II
C ) III only
D ) III and IV
E ) IV only

F x maths

Steps to derive

1 f(x) = sin 2x

2 f(- x) = sin 2(- x) = - sin 2x

3 f(- x) = - f(x)

4 f(x) is an odd function.
[If f(- x) = - f(x), then f(x) is an odd function.]

5 So, f(x) is symmetric about origin.

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Slope Formula

Sine formula

Graphing Equations

Graphing Equations:

Example issues for graphing equations help – linear equation:

Graph the linear equation y = 3x – 6
Solution:

To graph the linear equation they must find the x and y intercept of the linear equation. To find the x and y intercept they must plug the 0 for y and x.

From the above x intercept mean y = 0

So 0 = 3x – 6

3x = 6 and x = 2

So the x intercept point is (2, 0)

Now they must find the y – intercept so plug x = 0

y = 3 (0) – 6

y = -6


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Probability

Algebra graphing calculator

Free Fraction Help

Free fraction help:

1. In order to do fractions they first require to find the common factor of both the numerator and denominator (A common factor is any number that divides both the numerator and denominator). Like 3 divides 6 and 21.
2. Then continue dividing the fraction with the common factor till there's no more common factors in the numerator and denominator.
3. Now the fraction is called as simplified fraction as no common factors remaining which can divide both the numerator and denominator.

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Acute angle

Online square root calculator

Factors of 54

A ) 1, 2, 4, and 8
B ) 1, 2, 3, and 4
C ) 1, 2, and 4
D ) 1, 2, 4, 7, and 8


Steps to derive

1 56 = 1 × 56, 2 × 28, 4 × 14, 7 × 8
[Write the pairs of numbers with a product of 56.]
Factors of 64:

2 The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

3 64 = 1 × 64, 2 × 32, 4 × 16, 8 × 8
[Write the pairs of numbers with a product of 64.]

4 The factors of 64 are 1, 2, 4, 8, 16, 32, and 64.

5 68 = 1 × 68, 2 × 34, 4 × 17
[Write the pairs of numbers with a product of 68.]

6 The factors of 68 are 1, 2, 4, 17, 34, and 68.

7 The common factors of 56, 64 and 68 are 1, 2, and 4.

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Probability

Factors of 27

Polygons

Polygon definition:

A blocked flat surface shape among n sides is named polygon. There's n number of polygons are introduced in math. Side, vertex, diagonal, Interior angle, exterior angle are the parts of the polygon. Here Side is one of the line partitions that prepared a polygon. Vertex is a point in which one faces are meeting. And over one those points are called vertices. Diagonal is a line which is used to joining one vertices and it is not a side. Interior angle is angle which is produced by the one adjoining faces within the polygon. Exterior angle is a angle which is produced by one adjoining faces exterior the polygon.
Different Types of Polygons:
The given polygons are classified in to the basis of geometry. They are

* Regular polygon
* Irregular polygon
* Equiangular polygon
* Equilateral polygon
* Convex polygon
* Concave or non-convex polygon
* Crossed polygon.

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Geometry

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Pre calculus tutorials

Types of Prime Numbers

Types of Prime Numbers:(The prime numbers)
1. Balanced primes:
Prime numbers that ought to be the average of the earlier prime & following prime.In other words, earlier prime, prime itself, next prime ought to be in arithmetic progression.
Example:
5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103.....
2. Bell number primes:
These primes are the number of separations of a set with n members.
Example:
2, 5, 877, 27644437, 35742549198872617291353508656626642567....
3. Carol primes:
These type of primes are having the kind of (2n-1)2-2
Example:
47, 223, 3967, 16127, 1046527, 16769023, 1073676287, 68718952447....

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Hexagon problems

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Prime numbers

Pythagorean triples

Free triple 3

Question: Which of the following is not a Pythagorean triples?

A ) 5 cm, 10 cm, 12 cm
B ) 6 cm, 8 cm, 10 cm
C ) 3 cm, 4 cm, 5 cm
D ) 5 cm, 12 cm, 13 cm

The right answer is Option A
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Factors of 26
How to find factors of 70

Problems Factor calculator

Example Problems for factor by Grouping Calculator:

Problem 1:-

x³ – x² + x -1

Solution:-

first group the first and last two terms together like,

(x³ – x²) + (x - 1)

Now we can factor out x² from the first group and 1 from the second group.

x²(x - 1) + 1(x - 1)

now we can factor out (x - 1), so

(x - 1) (x² + 1)

Now the factors of x³ – x² + x -1 are (x - 1) (x² + 1)

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algebra help

Formula for mean

Types of Lines

Types of lines:

Perpendicular lines:

When the angle of 90 degree on two lines that two lines are said to be as perpendicular lines. This perpendicular line is represented as ‘_’. The perpendicular line does not have any postulates but solve some theorems. They are perpendicular lines and slopes theorem, perpendicular to parallel theorem and two perpendiculars theorem.

Parallel lines:

The separate two coplanar lines are called as parallel lines that are this line does not intersect with each other. The distance between the two lines are equal and it is represented as | |. The parallel lines are illustrating the two postulates.

Corresponding angles postulate: The angles are same when the transversal is cut the two coplanar lines. So we can say that lines are parallel.

Parallel lines postulate: If the transversal cut the two parallel lines, the same measure angles are present.