NCERT Class 12 Maths

You can use the position vector to find the real displacement of a point from a reference point.

Two vectors which are parallel to each other, irrespective of direction, are called parallel vectors.

Types are given below

• Collinear vectors
• Parallel vectors
• Antiparallel vectors

A vector with zero magnitude is considered a zero vector. Since it has no magnitude, its direction is considered arbitrary. This means the zero vector has no specific direction.

Below are a few important tips to remember the integrals of some particular functions:
1. Know the derivatives for each integral.
2. Make yourself familiar with the standard formulas first.
3. Practice daily for better memory.
4. Group similar formulas

Students can find the formula of integration for a particular function in this article. It is important to memorise these formulas to solve the integral problem easily. Below is the integration of a particular function formula.

The formula of a particular function:

1. Power Rule: 

$\int x^{n}dx=\frac{x^{n+1}}{n+1}+C(n\ne -1)$

2. Reciprocal Function:

$\int \frac{1}{x}dx=ln\left|x\right|+C$

3. Trigonometric Function: 

• $\int sinxdx=-cosx+C$
• $\int cosxdx=sinx+C$
• $\int {sec}^{2}xdx=tanx+C$
• $\int {csc}^{2}xdx=-cotx+C$
• $\int secxtanxdx=secx+C$
• $\int cscxcotxdx=-cscx+C$

4. Inverse Trigonometric Function

• $\int \frac{1}{1+x^2}dx={tan}^{-1}x+C$
• $\int \frac{1}{\sqrt{1-x^2}}dx={sin}^{-1}x+C$
• $\int \frac{-1}{\sqrt{1-x^2}}dx={cos}^{-1}x+C$

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• NCERT revision notes cover each chapter in clear, easy-to-read summaries along with detailed concepts.
• These notes cover the entire CBSE syllabus in simple language, including important definitions, formulas, and examples for the exams.
• Our subject matter experts have designed information in a genuine and concise way.
• These notes are perfect guides for both quick revision and thorough conceptual understanding.

Shiksha's NCERT notes are extremely useful for efficient preparation. We offer structured chapter-wise notes for the latest CBSE  syllabus and provide concise summaries and key formulas. These notes are designed for quick and last-minute revision. These short revision notes offer step-by-step explanations for conceptual clarity and include important questions from previous years' papers and NCERT Textbooks. Our notes are equally beneficial for competitive exams like JEE Mains, NEET and other exams as well.

All students work hard to get a full score. Here are a few tips that can make your dream come true.

• Master the concepts from the NCERT textbook before using any other notes and mark importnt points.
•  Consistentantly practice problems, highlight important formulas and theorems, and creating a personalized formula sheet.
• Regular- daily and weekly revision of the important concepts and formulas.
• Solve all examples and practice questions given in NCERT Textbooks.