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 .
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)
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 .
So you are given that and . You are asked for the value of . To do that you need to know that "integration is linear"- that is that .
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, or . I have assume the latter. Fortunately, for this problem, as long as all integrations are in the same order, it does not matter.
Apparently you are using "I= B(y)dy" to indicate - not very good notation- that "=" really doesn't belong there!(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)
The integration by parts formula, which you are clearly expected to know, is
.
Here, you have several different choices for "u" and "dv". Simplest is probably and
Okay, if what is ?(iii) Integrate I = ((9x^2)/((1-x^3)^0.5)) by using substitution u = 1 - x^3
Just at a wild guess you might try !! 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)