Question

∫_(-2)^3〖m^3 〖 (5+ m^4)〗^7 dm〗evaluate

Answer 1

YOu can use a u-sub here. :)

Answer 2

\[\int\limits_{\neg2}^{3}\]

Answer 3

-2 is the sub

Answer 4

\[〖m^3 〖 (5+ m^4)〗^7 dm〗\]

Answer 5

wolfram spits out huge answer for integral

Answer 6

No I mean "You can use the technique of substitution".

let u = 5 + m^4 and then du = 4m^2 dm

Answer 7

how would you work that out

Answer 8

http://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleIndefinite.aspx

Answer 9

Okay. let u=5+m^4
\[\frac{d}{dm}(u=5+m^4)\rightarrow \frac{du}{dm}=5m^3 \implies du=5m^3 dm \implies frac{du}{5}=m^3dm\]
Well you have an m^3 dm and a 5+m^4.
Replace that making your integral:
\[\frac{1}{5} \int\limits u^7 du=\frac{1}{40}u^8 \rightarrow \frac{1}{40}(5+m^4)^8\]
Now evaluate it:
\[\frac{1}{40}(5+m^4)^8|_{-2}^{3}=\frac{1}{40}[(5+(3)^4)^8-(5+(-2)^4)^8]=9.35*10^{13}\]

Answer 10

That last part of the first one should read:
\[\frac{du}{5}=m^3 dm\]