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Integration using Trigonometric Identities Video Lecture | Mathematics (Maths) Class 12 - JEE

204 videos|288 docs|139 tests

FAQs on Integration using Trigonometric Identities Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What are trigonometric identities used for in integration?
Ans. Trigonometric identities are used in integration to simplify trigonometric expressions and make them easier to integrate. By using these identities, we can transform complex trigonometric functions into simpler forms that can be more easily integrated.
2. Can you provide an example of using a trigonometric identity in integration?
Ans. Sure! One common example is the integration of the function ∫sin^2(x) dx. By using the trigonometric identity sin^2(x) = (1 - cos(2x))/2, we can rewrite the integral as ∫(1 - cos(2x))/2 dx. This simplification allows us to integrate the function more easily.
3. How can trigonometric identities help solve integrals involving trigonometric functions?
Ans. Trigonometric identities can help solve integrals involving trigonometric functions by transforming the original function into a simpler form that is easier to integrate. These identities allow us to apply known integration techniques or substitute variables, making the integration process more manageable.
4. Are there any specific trigonometric identities that are frequently used in integration?
Ans. Yes, there are several trigonometric identities that are commonly used in integration. Some of the frequently used identities include the Pythagorean identities (sin^2(x) + cos^2(x) = 1), double angle identities (such as sin(2x) = 2sin(x)cos(x)), and power-reducing identities (such as sin^2(x) = (1 - cos(2x))/2).
5. Can trigonometric identities be used to solve all types of integrals involving trigonometric functions?
Ans. While trigonometric identities are powerful tools in integration, they may not be sufficient to solve all types of integrals involving trigonometric functions. In some cases, other integration techniques or methods may be required, such as substitution, integration by parts, or special trigonometric substitutions. However, trigonometric identities often play a crucial role in simplifying the integrals and making them more approachable for these techniques.
204 videos|288 docs|139 tests

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