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cherrilyn

  • 5 years ago

with reduction formula and techniques, evaluate the integral of cos^2(sint)costdt

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  1. anonymous
    • 5 years ago
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    let u = cost and du = sint ^_^ that's all, give it a try now

  2. cherrilyn
    • 5 years ago
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    thanks! I'll try it now

  3. cherrilyn
    • 5 years ago
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    If u = cost and du=sint...what should I do with the cos^2?

  4. anonymous
    • 5 years ago
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    u = sint, du =cost dt. Then from here it becomes cos^2(u) du. Which turns into cos(u)*cos(u) which you can integrate with integration by parts.

  5. anonymous
    • 5 years ago
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    good luck :) np

  6. anonymous
    • 5 years ago
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    cos^2 = u^2 :)

  7. anonymous
    • 5 years ago
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    ^_^ substitute cos x with u

  8. cherrilyn
    • 5 years ago
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    so u = cos x not cos t?

  9. anonymous
    • 5 years ago
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    lol cost :)

  10. anonymous
    • 5 years ago
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    here : \[\int\limits \cos^2 t (cost) (sint) dt =-\int\limits u^3 du \rightarrow = - \frac{u^4}{4} + c \] \[= \frac{\cos^4 t}{4} + c\] better ? :)

  11. anonymous
    • 5 years ago
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    I forgot the minus in the last step, add it ^_^

  12. anonymous
    • 5 years ago
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    remember u = cos t, so du= - sin t

  13. cherrilyn
    • 5 years ago
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    yes! thank you so much :)

  14. anonymous
    • 5 years ago
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    np ^_^

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