Tuesday, 7 October 2014

calculus - Definite Trig Integrals: Changing Limits of Integration



π/40sec4θtan4θdθ



I used the substitution: let u=tanθ ... then du=sec2θdθ.



I know that now I have to change the limits of integration, but am stuck as to how I should proceed.




Should I sub the original limits into tanθ or should I let tanθ equal the original limits and then get the new limits?



And if it help, the answers of the definite integral is supposed to be 0.



Thanks in advance.


Answer



I=π/40sec4(θ)tan4(θ) dθ=π/40sec2(θ)(1+tan2(θ))tan4(θ) dθ=π/40tan4(θ) d(tanθ)+π/40tan6(θ) d(tanθ)=[15tan5(θ)]π/40+[17tan7(θ)]π/40=15+17=1235.


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