Chapter 11: Q. 40 (page 872)

Evaluate the integrals in Exercises 40–44.
$\int <t, t^{2}, t^{3}> d t$

Short Answer

Expert verified

The value for the given vector function is $<\frac{t^{2}}{2}, \frac{t^{3}}{3}, \frac{t^{4}}{4}> + C$ .

Step by step solution

Step 1. Given Information

Given that, $\int <t, t^{2}, t^{3}> d t$ .

Let us assume $r (t) = <t, t^{2}, t^{3}>$

Step 2. Evaluating the given integral

Evaluation,

$\int r (t) d t = \int <t, t^{2}, t^{3}> d t = \int (t i + t^{2} j + t^{3} k) d t = i \int t d t + j \int t^{2} d t + k \int t^{3} d t = i (\frac{t^{2}}{2}) + j (\frac{t^{3}}{3}) + k (\frac{t^{4}}{4}) + C = <\frac{t^{2}}{2}, \frac{t^{3}}{3}, \frac{t^{4}}{4}> + C$

So, the value of the given vector function is $<\frac{t^{2}}{2}, \frac{t^{3}}{3}, \frac{t^{4}}{4}> + C$ .

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Evaluate the integrals in Exercises 40–44.
$\int <t, t^{2}, t^{3}> d t$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Evaluating the given integral

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Evaluate the integrals in Exercises 40–44.∫t,t2,t3dt

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Evaluating the given integral

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Evaluate the integrals in Exercises 40–44.
$\int <t, t^{2}, t^{3}> d t$