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Evaluate the definite integral. ( Bite ' jtik) at (13 - 1) i - (e-] - 1) j+z k O e13 13 i- elj+z O e13 13 it (e-1 - 1) itz k O e13 13 ( e-1 - 1 ) +7 O e13 13 i - (e-] - 1) j+5 k e Textbook and Media Hint Assistance Used If r ( t ) = x( t ) it y (t) j + z(1) k. then / rend = (f "x(ndi) i+ ( f "vendi) ; + ( " =(ndi) k.Calculate d dt [ri(t) . r2(t)] and dt [ri(t) x r2(t)] first by differentiating the product directly and then by applying the formulas d dr 2 dri . r2(t) and dt [ri(t) . r2(t) ] = ri(t) dt dt d ri(t) x r2(t)] = ri(t) x dr2 dr1 + dt dt dt X r2(t). ri(t) = 4ti + 8t j + 4t k, r2(t) = t' k d dt [ri(t) . r2(t) ] = d dt [ri(t) x r2(t) ] =Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when needed. r(t) = cos(at)i - In(t)j + vt - 2k; to = 3 Domain is: Choose one Choose one NOTE: Enter ms of i, j, and k. r (3) = ( , L , )Describe the graph of the equation. 1-: (63:)i8rj 0 It is a line in 2space that goes through the point (6, 0) and is parallel to the vector r = 8 i 3i. 0 It is a line in 2space that goes through the point (3, 8) and is parallel to the vector 1' = 6 i. 0 It is a plane in 2-space that goes through the point ( 3, 8) and parallel to the vector l' = 6j. O ltis a plane in 2-space that goes through the point (6, O) and is parallel to the vectorr = 3 i Bj. 0 It is a line in 2-space that goes through the point (6, 0) and is parallel to the vector r = 3 i 8]. Find the limit. NOTE: Enter the answer using round brackets. t2+1 1 1i = ?? H530 W) I Find T(t) and N(t) at the given point. r(t) = 9 cos(t)i + 9 sin(t)j; t = T = NFind the arc length of the parametric curve. = 4 cos(t), y = 4sin(t), z = 3t; 0