What are the main topics in calculus? {{ currentPage ? currentPage.title : "" }}

A lot of students opt to study mathematics but are unaware of the subjects that they would have to deal with in their courses. Calculus is very crucial to mathematics. It is something that students cannot skip once they have chosen to become a mathematics specialist. According to experts, that are a part of various companies providing calculus assignment help, students need to have a good grasp of these topics if they want to secure the highest grades.

Significant topics and subtopics in Calculus


Limit of a function means the estimation of the value that a function approaches as it gets closer and closer to a certain point.

The topics under limits that are essential are as follows:

  • Estimating limits from graphs

  • Continuity over an interval

  • Estimating limits from tables

  • Properties of limits

  • Squeeze theorem

  • Types of discontinuities

  • Continuity at a point

  • Removing discontinuities

  • Limits by direct substitution

  • Limits using algebraic manipulation

  • Limits at infinity

  • Immediate value theorem 


The concept of derivatives is similar to the concept of slope but here you may find the rate of increase or slope of curves.


Topics under derivatives that are significant are as follows: 

  • Average versus the instantaneous rate of change

  • Secant lines

  • Estimating derivatives

  • Differentiability

  • Power rule

  • Derivative rules

  • Combining the power rule with other derivative rules

  • Product rule

  • Quotient rule

  • Chain rule

  • Implicit differentiation

  • Differentiating inverse functions

  • Derivatives of inverse trigonometric functions

  • Strategy in differentiating functions

  • Differentiation using multiple rules

  • Second derivatives

  • Disguised derivatives

  • Logarithmic differentiation

Applications of derivatives that include:

  • Straight-line motion

  • Non-motion applications of derivatives

  • Approximation with local linearity

  • L’Hospital’s rule


It is basically the area underneath a function when it has been graphed.

Topics under integrals that are important are as follows:

  • Approximation with Riemann sums

  • The fundamental theorem of calculus and definite integrals

  • Reverse power rule

  • Indefinite integrals of common functions

  • Summation notation

  • Riemann sums in summation notation

  • Defining integrals with Riemann sums

  • The fundamental theorem of calculus and accumulation functions

  • Interpreting the behaviour of accumulation functions

  • Properties of definite integrals

  • Definite integrals of common functions

  • Integrating with u-substitution

  • Integrating using long division and completing the square

  • Integration using trigonometric identities

Applications of integrals that include:

  • The average value of a function

  • Straight-line motion

  • Non-motion applications of integrals

  • Volume: Rectangles and squares cross-sections

  • Volume: Semicircles and triangles cross-sections

  • Area: the vertical area between curves

  • Area: the horizontal area between curves

  • Area: curves that intersect at more than two points

  • Volume: disc method (revolving around x- and y-axes)

  • Volume: disc method(revolving around other axes)

  • Volume: washer method (revolving around x- and y- axes)

  • Volume: washer method (revolving around other axes)

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