Hi! so i did this number and i have two things.
- the answer is 5pi/16 but i got over 4... anyone knows where my mistake could be?
- is there a way to do this a lot faster? i cant tell if this is how i should always do it or its way too long
#Trigonometric Integrals and Substitutions
deep sinew
high rivetBOT
deep sinew
<@&286206848099549185>
cobalt wing
In your textbook there should be a topic about signs of cos and sin
what to do when the exponents is odd, even, etc
It’s easy to make mistakes when you do intermediate steps in your head
deep sinew
In your textbook there should be a topic about signs of cos and sin
yes
i fixed that mistake
but it gave me at the end pi/2
then i redid it again
i got pi/2
i cant get the right answer
ill send you my two solutions
<@&286206848099549185>
cobalt wing
you forgot the bounds of integration
if you do u(pi) and u(0) you dont have to resubstitute the value of u after evaluating integral. if you keep same bounds you have to resubstitute. if you do double u substitution keep track like a book keeper or a russian egg doll
\begin{align}
\int_{0}^{\pi}cos^6xdx//
&= \frac{1}{8} \int_{0}^{2\pi}(1+cosu)^3du\
&= \frac{1}{16}\right(\int_{0}^{2\pi}du + 3\int_{0}^{2\pi}cosudu + \frac{3}&={2}\int_{0}^{2\pi} (1 + cos2u)du + 0 \left)\
&= \frac{1}{16} \left( u\bigl |{0}^{2\pi} + 3sinu \bigl |{0}^{2\pi} + \frac{3}{2}\left(u + \frac{1}{2}sin2u \right) \bigl |_{0}^{2\pi} \right)\
&= \frac{1}{16} (2\pi + \frac{3}{2}(2\pi)\
&= \frac{1}{16}(5\pi)
\end{align}
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jassmeene
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deep sinew
if you do u(pi) and u(0) you dont have to resubstitute the value of u after eval...
im so confused why do i need to change the limits giveno
i had a bunch of substitution rule exercices i never did it and i got it all right
cobalt wing
did you resubstitute the value of u at the end when evaluating the definite integral?
cobalt wing
how many times did you do substitution?
