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Evaluation of Definite Integrals using Substitution method Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Evaluation of Definite Integrals using Substitution method Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the substitution method in definite integration?
The substitution method is a technique used to evaluate definite integrals by making a change of variables. It involves substituting a new variable in place of the original variable in the integral, which simplifies the integral and makes it easier to evaluate.
2. How do I choose the appropriate substitution for a definite integral?
To choose the appropriate substitution for a definite integral, look for a part of the integrand that resembles the derivative of a function. This can be identified by patterns like power functions, exponential functions, trigonometric functions, or logarithmic functions. The substitution should simplify the integral and make it easier to solve.
3. Can you provide an example of evaluating a definite integral using the substitution method?
Certainly! Let's evaluate the definite integral ∫(2x + 3)² dx from 0 to 1 using the substitution method. We can first let u = 2x + 3. Taking the derivative of u with respect to x gives du/dx = 2. Rearranging this, we have dx = du/2. Substituting these values into the integral, it becomes ∫(u)² (du/2). Simplifying, we get (1/2) ∫u² du. Evaluating this integral gives us (1/2) * (u³/3) + C. Plugging in the limits of integration and simplifying further, we find the final answer to be 7/6.
4. Are there any tips or tricks for solving definite integrals using the substitution method?
Yes, there are a few helpful tips for solving definite integrals using the substitution method. One is to choose the substitution carefully, aiming to simplify the integral as much as possible. Another tip is to pay attention to the limits of integration and adjust them accordingly when substituting variables. Additionally, it can be useful to practice identifying patterns in integrands that suggest appropriate substitutions. Lastly, always remember to convert back to the original variable at the end to obtain the final answer.
5. Can the substitution method be used for all definite integrals?
No, the substitution method may not work for all definite integrals. Sometimes, the integral may not be easily simplified by a substitution or there may not be an obvious choice for the substitution variable. In such cases, other integration techniques like integration by parts or trigonometric identities may be more suitable. It's important to explore different methods and approaches to evaluate integrals effectively.
204 videos|288 docs|139 tests

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