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The velocity of a car was read from its speedometer at 10-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car.
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Calculus 1 / AB
Indefinite Integrals and the Net Change Theorem
Harvey Mudd College
University of Michigan - Ann Arbor
Idaho State University
In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.
In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.
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in this problem, It has given that the velocity of a car was read from the from its speedometer at 10 seconds intervals and recorded in the table. Use the midpoint rule to estimate the distance travelled by cars. Right? So what can we do here? Here is a table table given to us, right, for time and velocity we know the midpoint rule has been ruled that lT equals two given by b minus C. Buy it. Alright, so, remember here we are using midpoint with with five sub angels. Remember this. So for that and equals to where and is taking us five intervals. Okay, Right, so it will be what? 100? That is 100 means 100. Uh t in 2nd, 100 seconds has given 200 minus zero. It is given in the table divided by five. So, this will give me what This will give me 20 seconds. Right? Yeah. Okay, So now we need to calculate and are right because the velocity is given in miles but are so we need to convert it into uh okay. So don't forget to do so. So that's why I'm telling density is divided by delta. Isn't seconds. Okay, Then this should be divided by 3600 seconds. But isn't it? Because in one are 60 minutes are there? And in one minute it is 60 seconds out there. Right. So for in all total in an r 3600 seconds out there. Right. So this will give me what this will begin. This will be giving 20 seconds divided by 3600 seconds. But so this would give me yeah, one by 1 80. Hi. Yeah, isn't it? Yes. So what will be the mid points? Right. So here, 20 seconds is taken as a right? Uh this is one sub interval. Okay, so the mid points are taken. So midpoint is this, remember this is mid point, this is second interval. Right? All right. So here it is 10 then this will be third. Okay, So this is how we So I will be telling. So, this is coming as a midpoint in this way with little room for their things. Summit points will be got made. Points is given by what? This will be given by mm Again, 30. Then we have 10 30 50 70 90. Right? So 10 30, 50 70 and nice to you. All right, So, distance when we got distance equals two. One by vanity. Odd. Okay, distance is nothing. But this is velocity into types. So, this will give me like this. So 34 10 10 has velocity 34 MPH. Right? and similarly for 30 it's 54 miles better for 50 seconds. It should be 51 MPH. Then it is 55. Similarly for 76 70 seconds, and for 90 seconds it's 49. Alright? So here it will be the unit will be miles. But so this is going to be cut and this is going to be cut As so we will be getting the value in miles. So we will be getting 20-43 divided by 180. Who else? So this is giving me one point today. Five miles. All right. All you can say distance is approximately equal to 1.4 miles. So this is how we solve this problem. I hope you understood the concept. Thank you for watching. Yeah.
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