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Math Help - Intergration (can someone work out)

  1. #1
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    Intergration (can someone work out)

    i would greatly appreciate if someone could work these out for me, because im struggling and need some examples on how to intergrate

    bold letter are powers!

    y = 3x6


    y = 4x4 +3


    y = (5-3x)2


    Y = 5 sin 2x


    Y = cos 1 x
    3

    Y = 1 + √x
    x

    Y = e 3x + 7
    e x
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  2. #2
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    Some rules to help you.

     \int x^n~dx = \frac{x^{n+1}}{n+1}+C

     \int \sin kx~dx = -\frac{1}{k}\cos kx +C

     \int \cos kx~dx =\frac{1}{k}\sin kx +C
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    Cheers for that but i really need some worked examples so i can contnue with my project
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  4. #4
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    Follow this for your first question,

    \int 9x^2~dx = \frac{9x^{2+1}}{2+1}+C= \frac{9x^{3}}{3}+C= 3x^3+C

    what do you get?
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    3x7 + c i get to here then dont know what to do?
    7
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  6. #6
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    Quote Originally Posted by cjdyer View Post
    3x7 + c i get to here then dont know what to do?
    7
    You are finished, this is correct, try the next one.
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  7. #7
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    4x5 + c?
    5
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  8. #8
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    Quote Originally Posted by cjdyer View Post


    y = 4x4 +3


    Here's another example to follow

    \int 5x^3+7~dx = \frac{5x^{3+1}}{3+1}+7x+C=\dots

    The reason for this being

    \int a~dx=ax+C for a,C\in\mathbb{R}

    Quote Originally Posted by cjdyer View Post




    y = (5-3x)2

    And another example for this

    Expanding first (4-2x)^2 = (4-2x)(4-2x) = 16-16x+4x^2

    Now find \int 16-16x+4x^2~dx
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  9. #9
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    Quote Originally Posted by pickslides View Post
    Some rules to help you.

     \int x^n~dx = \frac{x^{n+1}}{n+1}+C

     \int \sin kx~dx = -\frac{1}{k}\cos kx +C

     \int \cos kx~dx =\frac{1}{k}\sin kx +C
    Two more rules you'll need:

     \int e^x~dx = e^x

    Assuming u = g(x)  \int f(u)u'~dx = \int f(u)~du

    u in this example then acts like x in the above four.

    Example of the last one (I know it's confusing)

    \int 5 \sin 2x ~ dx

    Here u = 2x so u' = 2

    So \int \frac{5}{2} \sin (u)u' ~ dx = \int \frac{5}{2} \sin (u) ~ du

    = \frac{5}{2}(-cos(u)) + C

    = - \frac{5}{2}cos(2x) + C
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  10. #10
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    For the last question

     y= \frac{e^{3x}+7}{e^x}= \frac{e^{3x}}{e^x}+ \frac{7}{e^x} = e^{2x}+7e^{-x}<br />
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  11. #11
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    Quote Originally Posted by cjdyer View Post
    i would greatly appreciate if someone could work these out for me, because im struggling and need some examples on how to intergrate
    bold letter are powers!
    Why not learn to post in symbols? You can use LaTeX tags.
    [tex]x^5+9=2[/tex] gives  x^5+9=2 .
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