math456
Can anyone help me with solving this integral?



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math456
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\[\int\limits_{2}^{5} (42x)dx\]

amistre64
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which part is giving you night terrors?

math456
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lol the 2nd one!

amistre64
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what is the integration rule for x^n ?

math456
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\[\int\limits_{2}^{5} 4.dx  2\int\limits_{2}^{5}x.dx\]

amistre64
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or you can think of it in terms of derivatives; what is the derivative rule for x^n ?

math456
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nx^n1

amistre64
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good, now how would you undo that? which is all an integration is ... undoing a derivative

math456
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thats wht i am having trouble with!

amistre64
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divide by n and add 1 back to the exponent

amistre64
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\[x=x^1\]right?

math456
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x^1

math456
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yea

amistre64
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\[x^1=x^{21}\]so n=2 in this case

math456
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ohh yea right!

amistre64
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so, does x^2 derive down to 2x?

math456
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yea it will be 2x^21

math456
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but we need x!

amistre64
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but we already have a 2x

amistre64
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you dont HAVE to pull out the constant. In this case it acutally helps out

math456
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2x/2

amistre64
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\[\frac d{dx}x^2=2x\]
\[\int 2x~dx=x^2\]

math456
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ohh gotch yea so, its gona be like (52)^2

amistre64
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\[\int\limits_{2}^{5} 4.dx  \int\limits_{2}^{5}2x.dx\]
\[4x(5,2)  x^2(5,2)\]
\[[4(5)4(2)]  [(5)^2(2)^2]\]

math456
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so i was doing just 1 term of x

amistre64
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you were mixing up the subtraction and the function into an ungodly abomination :)

math456
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yea right, i got it now! Thank you very much.. :)

amistre64
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\[\int_{a}^{b} f(x)~dx=F(b)F(a)~NOT~F(ba)\]

math456
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9

amistre64
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208(254)
20825+4
24  33 = 9 yes

math456
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yayy.. thanks again!