Examples : Integration using Trigonometric Identities

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

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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

 1. What are trigonometric identities?
Ans. Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables within their domains. They are used to simplify expressions, prove other identities, and solve trigonometric equations.
 2. How are trigonometric identities used in integration?
Ans. Trigonometric identities are often used in integration to simplify the integrand and make it easier to evaluate. By applying appropriate trigonometric identities, the integrand can be transformed into a more manageable form, allowing for easier integration.
 3. Can you provide an example of integrating using trigonometric identities?
Ans. Certainly! An example of integrating using trigonometric identities is ∫sin^2(x) cos^3(x) dx. By applying the double-angle identity sin^2(x) = (1 - cos(2x))/2, the integral can be rewritten as ∫[(1 - cos(2x))/2] cos^3(x) dx. This simplifies the integrand and makes it easier to integrate.
 4. Are there any specific trigonometric identities commonly used in integration?
Ans. Yes, there are several commonly used trigonometric identities in integration. Some of them include the Pythagorean identities (sin^2(x) + cos^2(x) = 1), double-angle identities (sin(2x) = 2sin(x)cos(x)), and power-reduction identities (sin^n(x) = (1/2^n) ∑(k=0 to n) C(n, k) cos[(n-2k)x]).
 5. Are there any tips for effectively using trigonometric identities in integration?
Ans. Yes, here are a few tips: - Familiarize yourself with the common trigonometric identities and their derivations. - Look for opportunities to simplify the integrand using trigonometric identities before attempting integration. - When encountering complex expressions, try expressing them in terms of simpler trigonometric functions using appropriate identities. - Practice solving integration problems involving trigonometric identities to improve your proficiency.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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