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Video: Integration by Partial Fractions Video Lecture | Mathematics (Maths) Class 12 - JEE
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FAQs on Video: Integration by Partial Fractions Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is integration by partial fractions? |  |
Ans. Integration by partial fractions is a method used in calculus to decompose a rational function into simpler fractions. It allows us to integrate complicated expressions by breaking them down into smaller, more manageable components.
| 2. When is integration by partial fractions used? | |
Ans. Integration by partial fractions is commonly used when integrating rational functions, where the degree of the numerator is less than or equal to the degree of the denominator. It helps simplify the integration process by decomposing the rational function into fractions that are easier to integrate.
| 3. How does integration by partial fractions work? | |
Ans. Integration by partial fractions involves breaking down a rational function into a sum of simpler fractions. To do this, we first factorize the denominator of the rational function. Then, using the method of partial fractions, we express the rational function as a sum of fractions with unknown constants in the numerators. These constants are determined by equating the coefficients of the corresponding powers of x on both sides of the equation.
| 4. What are the steps involved in integration by partial fractions? | |
Ans. The steps involved in integration by partial fractions are as follows:
1. Factorize the denominator of the rational function.
2. Write the rational function as a sum of partial fractions, with unknown constants in the numerators.
3. Determine the values of the unknown constants by equating coefficients of corresponding powers of x.
4. Integrate each partial fraction separately.
5. Combine the results of integration to obtain the final answer.
| 5. Are there any special cases or conditions for integration by partial fractions? | |
Ans. Yes, there are a few special cases and conditions to consider when using integration by partial fractions:
- If the degree of the numerator is greater than or equal to the degree of the denominator, we need to perform polynomial long division before applying the method of partial fractions.
- If the denominator has repeated factors, we use a different approach called the method of repeated partial fractions.
- If the denominator cannot be factorized, integration by partial fractions may not be applicable. In such cases, other integration techniques may need to be used.
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Dec 26, 2024 Last updated |
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