Question

Need some help with integration:

Answer 1

See this question.
http://openstudy.com/study#/updates/582e6d50e4b0080d89d93266
Im confused as to how user Stamp came up with those derivatives for the x and i functions.

Answer 2

\(\color{blue}{\text{Originally Posted by}}\) @stamp
\[H( r(u) ) = -u^2i+2u^3j\]\[r'(u)=6u^2i-2uj\]
\[eq1*eq2=-10u^4\]\[\int -10u^4=-2u^5\]from 0 to 1 = -2
\(\color{blue}{\text{End of Quote}}\)

Answer 3

r(u) was given\[r=2u^3[i]-u^2[j]\]\[r'=dr/du\]\[=3(2u^2)[i]-2(u^1)[j]\]\[r'=6u^2[i]-2u[j]\]

Answer 4

more like\[r'=2(3u^2)[i]-(2u^1)[j]\]

Answer 5

dot product H, r\[H•r=[i]_H[i]_r+[j]_H[j]_r\]

Answer 6

\[H•r=-u^2(6u^2)+2u^3(-2u)\]\[=-6u^4+(-4u^4)\]\[H•r=-10u^4\]

Answer 7

integrate respect to u the H r dot product\[\int-10u^4=-10\int u^4=-10(\frac{u^5}{5})\]\[F(u)=-2u^5\]evaluate F(u) from 0 to 1 \[-2(1^5)--2(0^5)=-2\]