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Integration By Partial Fractions Video Lecture | Mathematics (Maths) for JEE Main & Advanced
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FAQs on Integration By Partial Fractions Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. How do you determine the partial fractions for a given rational function? |  |
Ans. To determine the partial fractions for a given rational function, you first need to factorize the denominator completely. Then, you express the rational function as a sum of simpler fractions with these factors as denominators.
| 2. When do we use the method of partial fractions in integration? | |
Ans. The method of partial fractions is used when the integral of a rational function can be simplified by breaking it down into simpler fractions. This method is particularly useful when the degree of the numerator is less than the degree of the denominator.
| 3. Can you explain the difference between proper and improper fractions in the context of partial fractions? | |
Ans. In the context of partial fractions, proper fractions have a degree of the numerator that is less than the degree of the denominator, while improper fractions have a degree of the numerator equal to or greater than the degree of the denominator. Proper fractions can be easily integrated using partial fractions, while improper fractions require additional steps.
| 4. What are the different types of linear factors that can appear in partial fractions? | |
Ans. Linear factors in partial fractions can be of the form (ax + b), where a and b are constants. These linear factors can be distinct, repeated, or irreducible over the real numbers, each requiring a specific approach when determining the partial fractions.
| 5. How do you handle repeated factors in partial fractions? | |
Ans. When dealing with repeated factors in partial fractions, you express each repeated factor as a separate fraction with increasing powers in the numerator, starting from 1 up to the multiplicity of the factor. This allows you to decompose the given rational function into simpler fractions for integration.
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Nov 22, 2024 Last updated |
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