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Online Teachers Registration

Teachers Registration Online: Join Al-Saudia Virtual Academy as an online tutor and earn from home. Get registered today for world-class tutoring services, suitable for experienced teachers.
Online Teachers Registration
Online Teachers Registration

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Mathematics Tutor USA

Mathematics Tutor USA

Call Us: +92-332-3343253

Skype Id: ascc576

Email at: info@pakistanonlinetuition.com


Mathematics Tutors USA

Online Mathematics Tutor for USA Curriculum

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Basics of Algebra
Equations and Inequalities
Linear Relations and functions 
System of equation and Inequalities
Quadratic Functions and Inequalities
Complex Numbers
Polynomial Functions 
General Function
Conic Sections
Radical Functions and Rational Exponents
Sequences and Series
Rational Expressions
Exponential and Logarithmic Functions
Basics of Geometry
Parallel Lines and the Coordinate Plane
Congruent Triangles
Properties of Triangles
Quadrilaterals and Polygons
Right Triangles
Surface Area and Volume
Basics of Calculus
Functions and Binary Relations
Graphs of Function and Relations
Straight Lines
The General Equations of Straight Lines
Sequence and Limit of Sequences
Limit of a Function

Mathematics Worksheets

 Integration Made Easy

By Masood Amir

Mathematics Worksheets

Mathematics Worksheets, ASVA provide calculus and Algebra worksheets.


To measure change or variation of a function with respect to the independent variable we use Calculus.

Differential Calculus: (Mathematics Worksheets)

Differrential Calculus used to measure change or variation of a function in a very small invterval of time.

Integral Calculus:

The branch of calculus used to measure changes or variation over an interval of independent variable, called Integral calculus, e.g to find length of curve, the area of region and the volume of a solid in a specified period of time.

The technique used to measure such changes or variation called “Integration” or “Antiderivatives”. It a reverse process of differentiation.

Mathematically, Integration  defined as “ If f’(x) represents the differential coefficient of f(x), we need to find f(x), if we have f'(x) or dy/dx.


Notation: ”∫” used to show the integration, it is a symbol of “S” derived from the word “Sum”. i.e. Integration is a process in which we have to sum up the derivatives over a specified interval and to find the function.

Techniques of Integration:

As we know that integration is the reverse process of differentiation, our problem is to find the function f(x) or Y, when f’(X) or dy/dx is given.

dy/dx = f’(X)

∫dy = ∫f ’(X)dx

Y= f(x) is our solution

Ist Formula of Integration (1st Rule of Integration)

Indefinite Integration:

Ist Formula of Integration (Ist Rule of Integration):

Let ∫ dy = ∫ xndx

y = xn+1/n+1  + C

Why “C”:

In the process of differentiation, we eliminate constant, as the derivative of a constant is “zero”.

So, In functions like Xn, Xn+ 6, Xn + 3 ,  Xn – K, the derivatives of all of them is Xn-1, in finding the anti derivative of  Xn-1we put a constant “C”, as we don’t know which constant was present in the original function, and  can be found If we have initial boundary values (Definite Integral).

Example: Solve ∫x3dx

Solution:        x3+1/3+1 + C   = x4/4 + C

Example: Solve ∫(x+ x2 + 5x + 6)dx

Solution:      ∫x3dx + ∫x2dx + ∫5xdx + ∫6dx

                         X4/4 + x3/3 + 5x2/2+ 6x + C

Worksheet # 1

Find the Integral of the following:

SET 1 

∫(x3-4x2+5x-6)dx                        ∫(3x5-4x3+3x2)dx

∫(ax5-bx4)dx                               ∫(x3/2-5x4/3+3x2)dx

∫(4√3x2 -2x)dx                            ∫(3x + 5x2 –x3/2-0.4x4)dx

∫(x(8x-1/2)dx                               ∫(2-x)(4+3x)dx

∫(x-3 + x-4)dx                               ∫(2x3-3)3x4dx

∫(4x7 + 3x12 -5x8 + 2x -1)dx          ∫(ax3 – bx2 + cx –d)dx

∫(1/x3 + 2/x2 -6)dx                        ∫(-3x-8 + 2√x)dx

∫((x3 -5)(2x + 5)dx                         ∫(7x-6 + 5√x)dx

Online Tuition

Tuition Pakistan

Online Tutor Pakistan

Al-Saudia Virtual Academy

Mathematics Notes

Mathematics Notes

Call Us: +92-332-3343253

Skype Id: ascc576

Email at: info@pakistanonlinetuition.com

Mathematics Notes: Optimized for Effective Learning

Mathematics Notes

Comprehensive Calculus Notes:

Our online Mathematics notes offer a comprehensive coverage of Calculus, ensuring a deep understanding of concepts like derivatives, integrals, and limits. These notes are designed to facilitate active learning and foster problem-solving skills.

Algebra Made Accessible:

With our online Algebra notes, students can master fundamental algebraic concepts, such as equations, inequalities, functions, and polynomials. The organized structure and clear explanations enable students to grasp complex topics with ease.

Unlocking Trigonometry:

Our Trigonometry notes provide a concise yet thorough overview of trigonometric functions, identities, and equations. The notes are enriched with real-world applications, aiding students in visualizing and applying trigonometry in various contexts.

Statistical Insights:

Our online Statistics notes equip students with the knowledge needed to analyze and interpret data effectively. From probability and distributions to hypothesis testing and regression analysis, these notes empower learners to become proficient statisticians.

Mechanics Demystified:

Our Mechanics notes delve into the world of classical mechanics, covering topics like kinematics, dynamics, and Newton’s laws. The active voice sentences and clear explanations facilitate a better understanding of physical phenomena and problem-solving techniques.
Complex Numbers
Quadratic Equations
Systems of Two Equations
Determinants and Inverse Matrices
Sequence and Series
Permutations and Combinations
Introduction to Probability
Mathematical Induction
The Binomial Theorem
Fundamental Trigonometry
Trigonometric Identities
Trigonometric Functions
Solutions of Triangles
Inverse Trigonometric Functions
and Trigonometric equations
Orthogonal Trajectory

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Optimize your learning experience with our comprehensive services, including math tuition, mathematics tutors, math tutoring, and mathematics notes. Our dedicated team ensures smooth transitions between topics, helping students grasp mathematical concepts with ease. By using appropriate transition words, we foster a cohesive learning environment that enables students to build a strong foundation in mathematics.

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