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Math Help - Uni Yr1 first week exam - Integration questions

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    Uni Yr1 first week exam - Integration questions

    HI, Uni starts next week and we have a first week paper to test our weaknesses. Integration has been a struggle at times but with the mock paper they have provided I am amiss with these 4 questions - sometimes not even understanding the actual question . Apologies for my notaion...

    Any help would be greatly appreciated.
    (i) Given that f & g are continous and that I = f(x) dx = 5 (limts 6 & 2) and I = g(x) dx = 9 (limits 6 & 2) calculate I = 4f(x) - g(x) dx (limits 2 & 6)

    (ii) Using method by parts to express I = y^2*log(y) dy (limits x & 1) in the form
    A(x) + I= B(y) dy (limits x & 1)

    (iii) Integrate I = ((9x^2)/((1-x^3)^0.5)) by using substitution u = 1 - x^3

    (iv) Find a suitable substitution of the form y = f(x) for I = x^3*e^(-x^2) dx (limits infinity & 0)
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    http://www.mathhelpforum.com/math-he...ial-19060.html
    Why not learn to post in symbols? You can use LaTeX tags.
    [tex]\int_6^2 {f(x)dx} = 5[/tex] gives \int_6^2 {f(x)dx}  = 5.
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    Quote Originally Posted by dojo View Post
    HI, Uni starts next week and we have a first week paper to test our weaknesses. Integration has been a struggle at times but with the mock paper they have provided I am amiss with these 4 questions - sometimes not even understanding the actual question . Apologies for my notaion...

    Any help would be greatly appreciated.
    (i) Given that f & g are continous and that I = f(x) dx = 5 (limts 6 & 2) and I = g(x) dx = 9 (limits 6 & 2) calculate I = 4f(x) - g(x) dx (limits 2 & 6)
    So you are given that \int_2^6 f(x)dx= 5 and \int_2^6 g(x) dx= 9. You are asked for the value of \int_2^6 4f(x)- g(x) dx. To do that you need to know that "integration is linear"- that is that \int af(x)+ bg(x) dx= a\int f(x)dx+ b\int g(x)dx.

    By the way, just saying that the limits are "6 & 2" doesn't tell us whether the integral is from 6 to 2" or vice-versa. That is, \int_6^2 or \int_2^6 . I have assume the latter. Fortunately, for this problem, as long as all integrations are in the same order, it does not matter.

    (ii) Using method by parts to express I = y^2*log(y) dy (limits x & 1) in the form
    A(x) + I= B(y) dy (limits x & 1)
    Apparently you are using "I= B(y)dy" to indicate \int B(y)dy- not very good notation- that "=" really doesn't belong there!
    The integration by parts formula, which you are clearly expected to know, is
    \int u dv= uv- \int v du.
    Here, you have several different choices for "u" and "dv". Simplest is probably u= ln(y) and dv= y<br />
^2 dy

    (iii) Integrate I = ((9x^2)/((1-x^3)^0.5)) by using substitution u = 1 - x^3
    Okay, if u= 1- x^3 what is du?

    (iv) Find a suitable substitution of the form y = f(x) for I = x^3*e^(-x^2) dx (limits infinity & 0)
    Just at a wild guess you might try u= x^2!! what is du?
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