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Vector integration

16 practice questionsIntegral CalculusStep-by-step solutions

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1

Why must a constant vector C⃗\vec{C} (not just a constant scalar) be added when finding an indefinite integral of a vector function v⃗(t)\vec{v}(t)?

A.Because each of the three components has its own arbitrary constant of integration, which together form a constant vector
B.Because vector integrals never actually need a constant
C.Because C⃗\vec{C} must always be the zero vector for consistency
D.Because the constant only applies to the k\mathbf{k}-component
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2

Work done by a force F⃗\vec{F} moving a particle along a path CC from AA to BB is defined as which line integral?

A.W=∫CF⃗⋅dr⃗\displaystyle W=\int_C \vec{F}\cdot d\vec{r}
B.W=∫CF⃗×dr⃗\displaystyle W=\int_C \vec{F}\times d\vec{r}
C.W=∫C∣F⃗∣ dt\displaystyle W=\int_C |\vec{F}|\,dt
D.W=∫CF⃗ dt\displaystyle W=\int_C \vec{F}\,dt
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3

A particle has constant acceleration a⃗(t)=−10k\vec{a}(t)=-10\mathbf{k} (gravity) and initial velocity v⃗(0)=5i+20k\vec{v}(0)=5\mathbf{i}+20\mathbf{k}. Find v⃗(t)\vec{v}(t).

A.v⃗(t)=5i+(20−10t)k\vec{v}(t)=5\mathbf{i}+(20-10t)\mathbf{k}
B.v⃗(t)=5i−10t k\vec{v}(t)=5\mathbf{i}-10t\,\mathbf{k}
C.v⃗(t)=(5−10t)i+20k\vec{v}(t)=(5-10t)\mathbf{i}+20\mathbf{k}
D.v⃗(t)=5i+(20+10t)k\vec{v}(t)=5\mathbf{i}+(20+10t)\mathbf{k}
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