Find the integral $\int \left( 4 t \mathbf { i } + 6 t ^ { 2 } \mathbf { j } + 4 \mathbf { k } \right) d t$.
Select the correct answer.
A) $4 \mathbf { i } + 12 t \mathbf { j } + \mathrm { C }$
B) $4 t \mathbf { i } + 6 t ^ { 2 } \mathbf { j } + 4 \mathbf { k } + \mathbf { C }$
C) $2 t ^ { 2 } \mathbf { i } + 2 t ^ { 3 } \mathbf { j } + 4 t \mathbf { k } + \mathbf { C }$
D) $4 t ^ { 2 } \mathbf { i } + 6 t ^ { 3 } \mathbf { j } + 4 t \mathbf { k } + \mathbf { C }$

Question

Quizplus · Accepted Answer

The integral of a vector-valued function is the vector-valued function whose components are the integrals of the components of the original function. So,$$\int \left( 4 t \mathbf { i } + 6 t ^ { 2 } \mathbf { j } + 4 \mathbf { k } \right) d t = \int 4 t d t \mathbf { i } + \int 6 t ^ { 2 } d t \mathbf { j } + \int 4 d t \mathbf { k } = 2 t ^ { 2 } \mathbf { i } + 2 t ^ { 3 } \mathbf { j } + 4 t \mathbf { k } + \mathbf { C }$$

Find the Integral ∫(4ti+6t2j+4k)dt\int \left( 4 t \mathbf { i } + 6 t ^ { 2 } \mathbf { j } + 4 \mathbf { k } \right) d t∫(4ti+6t2j+4k)dt

Find the Integral $\int \left( 4 t \mathbf { i } + 6 t ^ { 2 } \mathbf { j } + 4 \mathbf { k } \right) d t$