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Problem

Evaluate the integral. $ \displaystyle \int^4_…

00:39

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Problem 28 Easy Difficulty

Evaluate the integral.
$\int_{0}^{4}(4-t) \sqrt{t} d t$


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01:28

Frank Lin

00:37

Amrita Bhasin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Related Topics

Integrals

Integration

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Top Calculus 1 / AB Educators
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Lectures

Video Thumbnail

05:53

Integrals - Intro

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.

Video Thumbnail

40:35

Area Under Curves - Overview

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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Watch More Solved Questions in Chapter 5

Problem 1
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Problem 5
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Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
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Problem 18
Problem 19
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Problem 21
Problem 22
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Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
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Problem 34
Problem 35
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Problem 37
Problem 38
Problem 39
Problem 40
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Problem 43
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Problem 45
Problem 46
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Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
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Problem 59
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Problem 64
Problem 65
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Problem 69
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Problem 75
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Problem 79
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Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86

Video Transcript

Alright, here's a fun integral. Um There's a lot of different kind of cleanup techniques which can help with. First we look and we think oh you stuff doesn't work as nice as I'd like and so you you need another technique. So there's one technique is called distribution. So basically I'm going to distribute the root tea to both parts That will give me four, can steer the one half minus T to the three halves, I'm converting to exponent form, so I can do reverse power roll. Yeah okay so that will give me then four times t to the three halves over three halves by reverse power roll minus 10 to the five halves over five halves. Um Then I can plug in my limits. So let's clean up just a little bit. This will be 8/3 cheated. The three has minus 2/5 T to the 5/2 and I still have to plug in my limits. So when I plug in four I get 8/3 4 to the 3/2ves minus 2, 54 to the five halves. And then the other terms will be zero when I plug in. So I'm done with that part. Now I'm just going to clean this up a little bit, this is eight thirds now four to the three halves, I can square root first for two and then go to the eight. So that's eight. Then for the four to the five halves I can square root to get two to the fifth is 32. Um Okay so I get 64/3 minus 64/5. And our final answer, if I clean that common denominator is 128 over 15. So that is then my solution to the integral anyway. Hopefully that helped have an amazing day.

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Calculus: Early Transcendentals

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Top Calculus 1 / AB Educators
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Harvey Mudd College

Caleb Elmore

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Kristen Karbon

University of Michigan - Ann Arbor

Calculus 1 / AB Courses

Lectures

Video Thumbnail

05:53

Integrals - Intro

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.

Video Thumbnail

40:35

Area Under Curves - Overview

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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