I m feeling difficulty in doing Indefinite Integration. please help!

Question

Answer

Guide to Indefinite Integration

Introduction

Indefinite integration is a mathematical technique used to find the antiderivative of a function. In other words, it is the process of finding a function whose derivative is the given function. Indefinite integration is an important concept in calculus and is used in various fields such as physics, engineering, and economics.

Steps for Indefinite Integration

To perform indefinite integration, follow the given steps:

Step 1: Identify the function to be integrated.

Step 2: Use the power rule, product rule, quotient rule, or chain rule to simplify the function.

Step 3: Find the antiderivative of the simplified function by reversing the rule used in step 2.

Step 4: Add the constant of integration (C) to the antiderivative to get the final solution.

Example

Suppose we want to find the antiderivative of the function f(x) = 2x + 3. Here are the steps to follow:

Step 1: Identify the function to be integrated: f(x) = 2x + 3

Step 2: Simplify the function using the power rule: ∫(2x + 3) dx = 2∫x dx + 3∫1 dx

Step 3: Find the antiderivative of the simplified function by reversing the rule used in step 2: 2∫x dx = x^2 + C1, 3∫1 dx = 3x + C2

Step 4: Add the constants of integration to the antiderivative to get the final solution: ∫(2x + 3) dx = x^2 + 3x + C

Conclusion

Indefinite integration can be a challenging concept to understand, but with practice, it can become easier. Remember to follow the steps, simplify the function, find the antiderivative, and add the constant of integration to get the final solution.

Answer

Just differentiate the answer and try to adjust the answer

Answer

Final value -initial value of the integrated function

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