Find the integral $\int \left( 4 t \mathbf { i } + 6 t ^ { 2 } \mathbf { j } + 4 \mathbf { k } \right) d t$
A) $4 \mathbf { i } + 12 t \mathbf { j } + \mathbf { C }$
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 each component is calculated separately: $\int 4t \, dt = 2t^2$, $\int 6t^2 \, dt = 2t^3$, and $\int 4 \, dt = 4t$. Adding the constant vector $\mathbf{C}$, the result is $2 t ^ { 2 } \mathbf { i } + 2 t ^ { 3 } \mathbf { j } + 4 t \mathbf { k } + \mathbf { C }$.

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