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hms.tech
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It might be difficult for you to read this integral in non latex form, but i'll try my best.
As i don't know how to write this in latex form, assume "for this problem" that I(n) is pronounced as "I subscript n" or nth term of I.
I(n)=∫ (sinx)^n dx [with limits of the integral as : from zero (0) to ∏/2 (pi/2)
Using the above equation, it is required to prove that :
I(n+2)= I(n) * (n+1)/(n+2) [again , I(n) means I subscript n ie nth term of a sequence]
the formula for integration by parts
I have tried to integrate it by parts using various ways but all of them failed to prove the required result.
One of them was :
∫ [sin^-2(x)*(sin(x))^(n+2)] dx [with the same limits ofcourse]
even after subsituting 1-cos^2(x) for sin^2(x) the problem could not be solved,
please help me solve it.
As i don't know how to write this in latex form, assume "for this problem" that I(n) is pronounced as "I subscript n" or nth term of I.
Homework Statement
I(n)=∫ (sinx)^n dx [with limits of the integral as : from zero (0) to ∏/2 (pi/2)
Using the above equation, it is required to prove that :
I(n+2)= I(n) * (n+1)/(n+2) [again , I(n) means I subscript n ie nth term of a sequence]
Homework Equations
the formula for integration by parts
The Attempt at a Solution
I have tried to integrate it by parts using various ways but all of them failed to prove the required result.
One of them was :
∫ [sin^-2(x)*(sin(x))^(n+2)] dx [with the same limits ofcourse]
even after subsituting 1-cos^2(x) for sin^2(x) the problem could not be solved,
please help me solve it.