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Solve the given problems by integration.The velocity $v$ (in $\mathrm{cm} / \mathrm{s}$ ) of an object is $v=\cos ^{2} \pi t .$ How far does the object move in $4.0 \mathrm{s} ?$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 5

Other Trigonometric Forms

Integrals

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:39

Give the velocity $v=d s /…

01:09

Find the position function…

00:54

01:37

Find the velocity, speed, …

03:52

Find the velocity, acceler…

01:12

Given the following veloci…

06:16

Position from velocity Con…

01:42

03:42

07:35

Additional ProblemsThe…

Okay, so we know that the velocity is a function of time, which is the derivative of position is to over pi. And then because sign of two TV over pi Okay, we also know that s of pi squared. It was one. So we start by finding Nance I derivative of this function because they're looking for us. We know it's prime. So if we look well, where did this two of her pie come from? When I'm taking the derivative What camp? In the Chambal, I took the derivative of something specifically something our co signs of Probably sign and then by the chain rule. So I got co sign and then multiplied by two over pie. So that should be an anti derivatives of this prime. And then if we add si, this is representing all such anti derivatives. But we need to find the one that that satisfies this condition. If I plug in pi squared, I should get more a sign of two. I swear it over pi. Well, this is just sign it to pie. So we have one is zero Class C or C is one. So our position should be sign of two t over pi plus one

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In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Give the velocity $v=d s / d t$ and initial position of an object moving alo…

Find the position function $s(t)$ from the given velocity or acceleration fu…

Find the velocity, speed, and acceleration at the given time t of a particle…

Find the velocity, acceleration, and speed of a particle with the given posi…

Given the following velocity functions of an object moving along a line, fin…

Position from velocity Consider an object moving along a line with the given…

Find the position function from the given velocity or acceleration function.…

Additional ProblemsThe position of a particle as it moves along a $y$ ax…

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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