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Integrals involving Exponential Functions Video Lecture | Mathematics (Maths) Class 12 - JEE

204 videos|288 docs|139 tests

FAQs on Integrals involving Exponential Functions Video Lecture - Mathematics (Maths) Class 12 - JEE

1. How do you integrate exponential functions?
Ans. To integrate exponential functions, you can use the formula: ∫e^x dx = e^x + C where C is the constant of integration.
2. Can you provide an example of integrating an exponential function?
Ans. Sure! Let's integrate the function ∫2e^x dx. Using the formula, we have: ∫2e^x dx = 2∫e^x dx = 2(e^x) + C So, the integral of 2e^x is 2e^x + C.
3. Is there a specific method to integrate exponential functions with a constant as the base?
Ans. Yes, if you have an exponential function with a constant base, such as ∫a^x dx, you can use a logarithmic transformation. The integral formula is: ∫a^x dx = (a^x / ln(a)) + C where ln(a) represents the natural logarithm of the base a.
4. Can you explain how to integrate a function that is the product of an exponential function and another function?
Ans. Yes, to integrate a function of the form ∫f(x)e^x dx, you can use integration by parts. The formula is: ∫u dv = uv - ∫v du Let u be the function f(x) and dv be e^x dx. Differentiate u to find du and integrate dv to find v. Then, apply the integration by parts formula to evaluate the integral.
5. Are there any special techniques for integrating more complex exponential functions?
Ans. Yes, some techniques for integrating more complex exponential functions include substitution and partial fraction decomposition. These methods can be helpful when the integrand involves a combination of exponential functions, trigonometric functions, or other algebraic terms. It's important to analyze the specific form of the integral and choose the most appropriate technique based on its structure.
204 videos|288 docs|139 tests

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