Question

integral from 0 to 1 of
(t(e^(-t^2))i+tln((t^2)+1)j) dt
@ganeshie8 hello? ._.

Answer 1

\[\int\limits_{0}^{1} \left( te ^{-t ^{2}} i+tln \left( t ^{2} +1 \right)j\right) dt\]

Answer 2

u sub on the i component
and int by parts on the j

Answer 3

so separate the integrals. then u sub for i and IBP for j. then just combine into a vector, right?

Answer 4

yea derivative of a vector is a vector and integral of a vector is a vector

Answer 5

@ganeshie8 I understand what he said to do but im just having computational problems :(

Answer 6

heyy

Answer 7

\[\int\limits_{0}^{1} \left( te ^{-t ^{2}} i+t\ln \left( t ^{2} +1 \right)j\right) dt\]

is same as

\[\left(\int\limits_{0}^{1} te ^{-t ^{2}} dt~\right)i+\left(\int\limits_{0}^{1} t\ln ( t ^{2} +1)~dt\right) j\]

Answer 8

evaluate each integral and plugin ?