Evaluate the definite integral below. $$\int _ { 0 } ^ { 2 } \left( - 6 t ^ { 2 } \mathbf { i } + 10 t ^ { 4 } \mathbf { j } + 15 t ^ { 4 } \mathbf { k } \right) d t$$
A) $- 16 \mathbf { i } + 64 \mathbf { j } + 64 \mathbf { k }$
B) $64 \mathbf { i } + 64 \mathbf { j } + 96 \mathbf { k }$
C) $64 \mathbf { i } + 128 \mathbf { j } + 64 \mathbf { k }$
D) $- 16 \mathbf { i } + 128 \mathbf { j } + 96 \mathbf { k }$
E) $- 16 \mathbf { i } + 64 \mathbf { j } + 96 \mathbf { k }$

Question

Quizplus · Accepted Answer

The integral of each component is calculated separately: $\int_{0}^{2} -6t^2 \, dt = -16$, $\int_{0}^{2} 10t^4 \, dt = 64$, and $\int_{0}^{2} 15t^4 \, dt = 96$.

Evaluate the Definite Integral Below ∫02(−6t2i+10t4j+15t4k)dt\int _ { 0 } ^ { 2 } \left( - 6 t ^ { 2 } \mathbf { i } + 10 t ^ { 4 } \mathbf { j } + 15 t ^ { 4 } \mathbf { k } \right) d t∫02​(−6t2i+10t4j+15t4k)dt

Evaluate the Definite Integral Below $\int _ { 0 } ^ { 2 } \left( - 6 t ^ { 2 } \mathbf { i } + 10 t ^ { 4 } \mathbf { j } + 15 t ^ { 4 } \mathbf { k } \right) d t$