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    https://gyazo.com/b1cd3f8a6c96dd2e4b5c9e67480c10e3

    Q5 (a) if you integrate it you would get - [integral ( e^-lambda.x) dx ] with limits
    of infinity and 0.

    How exactly do you tackle the question if you have limits of infinity?
    What exactly do I sub in or what happens in the answer?

    (b) i) you just differentiate via quotient rule but for ii) I don't have any clues
    or idea how to go about solving especially when I have infinity as my limit etc
    as I haven't been introduced this concept before. :s

    I'd appreciate any help.
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    (Original post by XxKingSniprxX)
    https://gyazo.com/b1cd3f8a6c96dd2e4b5c9e67480c10e3

    Q5 (a) if you integrate it you would get - [integral ( e^-lambda.x) dx ] with limits
    of infinity and 0.

    How exactly do you tackle the question if you have limits of infinity?
    What exactly do I sub in or what happens in the answer?

    (b) i) you just differentiate via quotient rule but for ii) I don't have any clues
    or idea how to go about solving especially when I have infinity as my limit etc
    as I haven't been introduced this concept before. :s

    I'd appreciate any help.
    You do the indefinite integral, and then take limits of the result as x goes to infinity minus the result as x goes to 0
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    (Original post by XxKingSniprxX)
    https://gyazo.com/b1cd3f8a6c96dd2e4b5c9e67480c10e3

    Q5 (a) if you integrate it you would get - [integral ( e^-lambda.x) dx ] with limits
    of infinity and 0.

    How exactly do you tackle the question if you have limits of infinity?
    What exactly do I sub in or what happens in the answer?

    (b) i) you just differentiate via quotient rule but for ii) I don't have any clues
    or idea how to go about solving especially when I have infinity as my limit etc
    as I haven't been introduced this concept before. :s

    I'd appreciate any help.
    Since this is an improper integral, it might be useful to first determine at which points the integral isn't very nicely defined - which is infinity here, then rewrite it as \displaystyle \lim_{a \to \infty} [ \int_0^{a} \lambda e^{-\lambda }.dx ] and take the integral as normal inside the limit then take the limit of it.

    Notice that the integral is just -\frac{\sin(x)}{x} from 0 to \frac{\pi}{4}. The expression is defined at x=\frac{\pi}{4} but not 0, so take the limit as that goes to 0 noting that we have \sin(x) \approx x for small x
 
 
 
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