Important Integration Formulas For JEE
In preparation for the Joint Entrance Examination (JEE) and other competitive exams, a solid understanding of integration and the relevant formulas is crucial. Here are some important integration formulas you should be familiar with:
Indefinite Integral of a Constant (C):
∫C dx = Cx + D, where C is a constant and D is the constant of integration.
Power Rule:
∫x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1.
Indefinite Integral of e^x:
∫e^x dx = e^x + C.
Indefinite Integral of a Sum or Difference:
∫[f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx.
∫[f(x) - g(x)] dx = ∫f(x) dx - ∫g(x) dx.
Indefinite Integral of Trigonometric Functions:
∫sin(x) dx = -cos(x) + C.
∫cos(x) dx = sin(x) + C.
Indefinite Integral of Secant and Tangent:
∫sec(x) dx = ln|sec(x) + tan(x)| + C.
∫tan(x) dx = -ln|cos(x)| + C.
Indefinite Integral of Cosecant and Cotangent:
∫csc(x) dx = -ln|csc(x) - cot(x)| + C.
∫cot(x) dx = ln|sin(x)| + C.
Indefinite Integral of Exponential Functions:
∫a^x dx = (1/ln(a)) * a^x + C, where 'a' is a positive constant.
Indefinite Integral of Hyperbolic Functions:
∫sinh(x) dx = cosh(x) + C.
∫cosh(x) dx = sinh(x) + C.
Indefinite Integral of Inverse Trigonometric Functions:
∫(1/√(1 - x^2)) dx = arcsin(x) + C.
∫(1/√(1 + x^2)) dx = arctan(x) + C.
Integration by Parts:
∫u dv = uv - ∫v du, where 'u' and 'dv' are differentiable functions of 'x'.
Integration by Substitution:
∫f(g(x)) * g'(x) dx = ∫f(u) du, where 'u' is a function of 'x' and du = g'(x) dx.
Leibnitz Theorem:
Definite integrals as a limit of sum:
A solid grasp of integration formulas is essential for excelling in the JEE examination, as well as for a deeper understanding of calculus, which forms the foundation of many scientific and engineering disciplines. By mastering these essential integration formulas, you'll not only be well-prepared for the exam but also equipped with valuable mathematical tools that will serve you throughout your academic and professional journey. Practice these formulas diligently, and you'll find that calculus, often considered a challenging subject, becomes a powerful and elegant tool in your problem-solving arsenal.
Important Integration Formulas For JEE FAQs
Q1. Why are integration formulas crucial for JEE?
Ans. Integration is a fundamental aspect of calculus, vital for solving problems in physics, math, and engineering. Mastery of these formulas is essential for JEE as they are commonly tested in the math section.
Q2. How can I effectively remember these integration formulas?
Ans. Memorizing these formulas can be tough, but practice is key. Solve diverse integration problems to reinforce your memory and understanding. Using flashcards or cheat sheets for regular review can also help.
Q3. Do these integration formulas apply solely to JEE, or are they used in other fields?
Ans. These integration formulas are foundational in calculus and find widespread use in math, physics, engineering, and science. They serve as the basis for solving a broad range of mathematical and real-world problems.
Q4. Can I use a calculator in the JEE exam for integration problems?
Ans. Typically, JEE has rules limiting calculator use, and advanced calculators with symbolic integration functions are not allowed. Be prepared to manually solve integration problems using these formulas.
Q5. Are there specific strategies for solving integration problems in the JEE exam?
Ans. Yes, it's essential to practice various integration problems. Familiarize yourself with different techniques like integration by parts and substitution, and learn when to apply them. Effective time management during the exam is crucial for efficient problem-solving.
