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if integration f(x)dx=g(x) then integrate x^5.f(x^3)
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if integration f(x)dx=g(x) then integrate x^5.f(x^3)
Integration of x^5.f(x^3)
Integrating a function of the form x^5.f(x^3) can be done by applying a change of variable. Let's denote u = x^3, then du = 3x^2 dx. We can rewrite the integral in terms of u as follows:
∫x^5.f(x^3) dx = ∫(1/3)u^(5/3) f(u) du
Now, we can see that the integrand resembles the form of the given integration f(x)dx=g(x). Therefore, we can rewrite the integral as:
(1/3)∫u^(5/3) f(u) du
This now simplifies to:
(1/3)g(u) + C
Finally, substituting back the variable u = x^3, we get:
(1/3)g(x^3) + C
Therefore, the integral of x^5.f(x^3) dx is equal to (1/3)g(x^3) + C.
Community Answer
if integration f(x)dx=g(x) then integrate x^5.f(x^3)
17 X raised to 9 - 5 x raised to 17 whole divided by 68
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if integration f(x)dx=g(x) then integrate x^5.f(x^3) for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about if integration f(x)dx=g(x) then integrate x^5.f(x^3) covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for if integration f(x)dx=g(x) then integrate x^5.f(x^3).
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