Find the Indefinite Integral Below $$\int \left( \frac { - 6 } { t ^ { 3 } } \mathbf { i } + 25 t ^ { 4 } \mathbf { j } + 4 t ^ { - 1 / 5 } \mathbf { k } \right) d t$$

question 50

Multiple Choice

Find the indefinite integral below. $$\int \left( \frac { - 6 } { t ^ { 3 } } \mathbf { i } + 25 t ^ { 4 } \mathbf { j } + 4 t ^ { - 1 / 5 } \mathbf { k } \right) d t$$
Do not include an arbitrary constant vector.

• A) \(\frac { 3 } { t ^ { 2 } } \mathbf { i } + 5 t ^ { 5 } \mathbf { j } + 5 t ^ { 4 / 5 } \mathbf { k }\)
• B) \(\frac { 3 } { t ^ { 2 } } \mathbf { i } + 5 t ^ { 5 } \mathbf { j } + 5 t ^ { 5 / 4 } \mathbf { k }\)
• C) \(\frac { 3 } { t ^ { 3 } } \mathbf { i } + 5 t ^ { 5 } \mathbf { j } + 5 t ^ { 4 / 5 } \mathbf { k }\)
• D) \(\frac { 3 } { t ^ { 2 } } \mathbf { i } + 5 t ^ { 5 } \mathbf { j } - 5 t ^ { 4 / 5 } \mathbf { k }\)
• E) \(- \frac { 3 } { t ^ { 2 } } \mathbf { i } + 5 t ^ { 5 } \mathbf { j } + 5 t ^ { 4 / 5 } \mathbf { k }\)

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Definitions:

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Subatomic particles with a negative electric charge, found in all atoms and acting as the primary carrier of electricity in solids.

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A fundamental component or base element used for constructing larger structures or systems.

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Variants of a particular chemical element which differ in neutron number, and consequently in nucleon number, but share the same number of protons.

Subatomic Particles

Particles that are smaller than an atom, including protons, neutrons, and electrons, which make up the atoms' structure.