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Thread: anti-derivative problems

  1. #1
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    Exclamation anti-derivative problems

    hi guys, i need help finding the anti-derivatives for these problems

    Any help woud be appreciated

    y' = tan(x)sec^2(x)

    y' = 3x^(-1/2)

    y' = -2cot^2(x)csc(x)
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by sess View Post
    hi guys, i need help finding the anti-derivatives for these problems

    Any help woud be appreciated

    y' = tan(x)sec^2(x)
    Make the substitution z=\sec x

    y' = 3x^(-1/2)
    Use the simple power rule...

    --Chris
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  3. #3
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    aight these are the answers that i got

    y' = tan(x)sec^2(x) -> y = sec^2(x)tan(x)

    y' = 3x^(-1/2) -> y = 1/(2x^(3/2))

    y' = -2cot^2(x)csc(x) -> y = 2 (ln(abs(sin(x))))(csc(x))

    did i get it?
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  4. #4
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    pls help me out guys
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  5. #5
    Super Member 11rdc11's Avatar
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    Take the derivative of your answer and if it matches your integral than it is right.

    The answer for the 1st is

    \frac{\sec^2{x}}{2} + c
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  6. #6
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    can u show me the steps on how u got that answer please?
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  7. #7
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by sess View Post
    can u show me the steps on how u got that answer please?
    \int \tan{x}\sec^2{x}~dx

    Like chris said

    \sec{x}= u

    \sec{x}\tan{x}dx=du

    \int u^{n}~du = \frac{u^{n+1}}{n+1} + C

    Can you finish up?
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  8. #8
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    ok Ive no idea wat u just said

    i do know that the first derivative of sec(x) is sec(x)tan(x) right?

    i also know that the first derivative of tan(x) is sec^2(x)

    Where do i go from here? I really must appologize to you 11rdc11
    I have not understood the concept of finding the anti-derivative at all

    Would you please be so kind and explain?
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  9. #9
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by sess View Post
    ok Ive no idea wat u just said

    i do know that the first derivative of sec(x) is sec(x)tan(x) right?

    i also know that the first derivative of tan(x) is sec^2(x)

    Where do i go from here? I really must appologize to you 11rdc11
    I have not understood the concept of finding the anti-derivative at all

    Would you please be so kind and explain?
    Ok do you know the basic integral formula

    \int u^{n}~du = \frac{u^{n+1}}{n+1} + C
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  10. #10
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    Quote Originally Posted by 11rdc11 View Post
    Ok do you know the basic integral formula

    \int u^{n}~du = \frac{u^{n+1}}{n+1} + C
    yep i understand that part
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  11. #11
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by sess View Post
    yep i understand that part
    Ok n just represents the power.

    So notice if we plug in the u of sub that I showed earlier the problem becomes the basic formula. Then just continue using the integral formula and back sub in the end.
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