Chapter 14: Q. 5 (page 1095)

Calculus of vector-valued functions: Calculate each of the following.
$\int r (t) d t, where r (t) = e^{t} i + t^{3} j - 4 k$

Short Answer

Expert verified

The value of $\int r (t) d t = e^{t} i + \frac{t^{4}}{4} j - 4 t k$

Step by step solution

Step 1.Given Information

Calculus of vector-valued functions: Calculate each of the following.

$\int r (t) d t, where r (t) = e^{t} i + t^{3} j - 4 k$

Step 2. Now finding the value of ∫r(t)dt

$\int r (t) d t = \int (e^{t} i + t^{3} j - 4 k) d t \int r (t) d t = (\int e^{t} d t) i + (\int t^{3} d t) j - 4 (\int d t) k \int r (t) d t = e^{t} i + (\frac{t^{4}}{4}) j - 4 (t) k \int r (t) d t = e^{t} i + \frac{t^{4}}{4} j - 4 t k$

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Calculus of vector-valued functions: Calculate each of the following.
$\int r (t) d t, where r (t) = e^{t} i + t^{3} j - 4 k$

Short Answer

Step by step solution

Step 1.Given Information

Step 2. Now finding the value of ∫r(t)dt

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Calculus of vector-valued functions: Calculate each of the following.∫r(t)dt,wherer(t)=eti+t3j−4k

Short Answer

Step by step solution

Step 1.Given Information

Step 2. Now finding the value of ∫r(t)dt

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

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Pure Maths

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Calculus of vector-valued functions: Calculate each of the following.
$\int r (t) d t, where r (t) = e^{t} i + t^{3} j - 4 k$