Integral Calculus

By : Manglika Tripathi

Updated : Feb 25, 2021, 17:40

Integral is an important concept in Calculus that can describe various concepts like volume, area, displacement, etc. Integral calculus is exactly the opposite of differential calculus and is an important concept of engineering mathematics. Integral Calculus has many real-life applications in various fields of engineering. Integral Calculus MCQ questions are also asked in the GATE exam under the section of engineering mathematics.

Integral Calculus GATE CS questions are asked in exams of other streams too. GATE EC, GATE ME, etc. exams also ask questions based on Integral Calculus. Read on to know more about the Integral Calculus syllabus for GATE.

Important Integral Calculus Topics for GATE CS



Indefinite Integration

All the anti-derivatives of any function are brought together in a set, forming the indefinite integral of that function.

Suppose there is a function named ‘f(x)’, then the indefinite integral of f(x) w.r.t. x is defined as:

∫fxdx=Fx+C where ‘C’ is termed as the constant of integration.

Definite Integration

Definite integration performs integration on any function or constant along with upper and lower limits. It can be used to find the area, displacement, etc. at given intervals. Suppose the area ‘A’ of a function f(x) is defined between the intervals ‘a’ and ‘b’. The area can also be represented as:

A = abfxdx

Integral of a Natural Exponential Function

The formula for calculation of integral of a natural exponential function is:

∫ex dx = ex + c

Integral of a General Form Polynomial Function

The integral of a polynomial function in general form is as follows:


If any number ‘k’ is introduced in the polynomial function, then the integral formula will change. A general form of polynomial function can be quadratic, cubic, etc. in terms of the degree of the equation.

Tips to Solve Integral Calculus Questions for GATE Exam

  • Practice previous years’ GATE questions with the help of Integral Calculus GATE questions and answers PDFs.
  • Practice many Integral Calculus quizzes to enhance your question-solving speed.
  • You should be well-rehearsed with the formulas, properties, and theorems used in Integral Calculus.
  • Make sure to revise all the Integral Calculus topics for GATE CS and other streams.

Importance of Integral Calculus in GATE CS

  • Integral Calculus for computer science has many real-life applications. Besides CS, Integral Calculus has real-life applications in many other fields such as astronomy, weather analysis, electric circuits, cost analysis, etc.
  • Integral Calculus GATE syllabus also tests the numerical and arithmetic skills of the applicants.
  • You will have to solve the Integral Calculus GATE questions in a limited time in the GATE exam. This will test your speed and accuracy of solving numerical problems.
  • Integral Calculus questions will test the engineering mathematics skills of the applicants.

Most Recommended Books for Integral Calculus for GATE CS

You should have the complete Integral Calculus study material for GATE CS before starting your preparation. Some of the best Integral Calculus books for GATE exam preparation are as follows:

Book Name


Advanced Engineering Mathematics

Erwin Kreyszig

Advanced Engineering Mathematics

RK Jain

Higher Engineering Mathematics

Bandaru Ramana

Why prepare Integral Calculus from BYJU'S Exam Prep?

More than 11 million students trust BYJU'S Exam Prep for competitive exam preparation. You can access Integral Calculus GATE notes for free on BYJU'S Exam Prep. You can find GATE notes streamwise on BYJU'S Exam Prep like Integral Calculus notes for CS, notes for ME, etc. One can also view/download Integral Calculus notes for GATE PDF or Integral Calculus MCQ PDF via BYJU'S Exam Prep. You can also test your performance by opting for various Integral Calculus online quizzes available on BYJU'S Exam Prep. One can also opt for paid subscriptions on BYJU'S Exam Prep to unlock unlimited test series.


Q. What would be the value of 0π/4xcos x2dx up to three decimal places? Assume that the value of π = 3.14.

The answer to the above integral would be from 0.27 to 0.30.

Q. What would be the value of ‘k’ in 02π|xsin x|dx=kπ ?

The value of k in the above numerical would be 4.

Q. What would be the value of the integral 0x2 cosxdx?

Apply the integral calculus procedures to obtain the given integral value, which comes out to be -2π (negative). One can also refer to the Integral Calculus online tests available on BYJU'S Exam Prep to know more about GATE FAQs

Q. Evaluate the value of 0π/41-tanx / (1 + tanx) dx according to the integral calculus rules.

You can apply the integral calculus standards to solve the given numerical. The answer to the given numerical comes out to be: (½ ln2) where ‘ln’ is the natural logarithm.

Q. Which property defines the solution of the Laplace equation as ∇2f = 0?

The property that defines the above solution is:

The Laplace solutions do not possess a maxima/minima at any point except boundaries.