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Use method of substitution to evaluate integration x(x2+4) power 5 dx?
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Use method of substitution to evaluate integration x(x2+4) power 5 dx?
Integration using Method of Substitution
When evaluating the integral of x(x2 + 4)5 dx using the method of substitution, we follow these steps:
- Select a substitution: Let u = x2 + 4. Then, du = 2x dx.
- Express the integral in terms of u: Substituting u back into the integral gives us ∫x * u5 / 2 du.
- Make the necessary adjustments: We need to rewrite the integral in terms of u and du. This involves replacing x and dx with expressions involving u and du.
- Integrate with respect to u: The integral becomes (1/2) * ∫u5 du.
- Integrate the new expression: Integrating u5 with respect to u gives u6 / 6.
- Undo the substitution: Replace u with x2 + 4 to get the final result.
By following these steps, you can evaluate the given integral using the method of substitution.
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Use method of substitution to evaluate integration x(x2+4) power 5 dx?
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Use method of substitution to evaluate integration x(x2+4) power 5 dx? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Use method of substitution to evaluate integration x(x2+4) power 5 dx? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Use method of substitution to evaluate integration x(x2+4) power 5 dx?.
Use method of substitution to evaluate integration x(x2+4) power 5 dx? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Use method of substitution to evaluate integration x(x2+4) power 5 dx? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Use method of substitution to evaluate integration x(x2+4) power 5 dx?.
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