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Use Part 1 of the Fundamental Theorem of Calculus…

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Problem 15 Easy Difficulty

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

$ \displaystyle y = \int^{3x + 2}_1 \frac{t}{1 + t^3} \,dt $


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Frank Lin

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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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
Problem 2
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Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
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Problem 45
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Problem 47
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Problem 49
Problem 50
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Problem 52
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Problem 55
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Problem 61
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Problem 66
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Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
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Problem 79
Problem 80
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Problem 82
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Problem 86

Video Transcript

Okay. We know we can use the chin rule. So we have three exposed to remember that per the fundamental fear of calculus, the teas now get substituted with excess and then the derivative of through exports to we know the cowfish in front of the exes. Three Therefore, we multiply this by three, which simplifies to be nine exports sex because it's three times three and then three times too. Don't forget, this multiplies by both thus and thus.

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Lectures

Video Thumbnail

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Video Thumbnail

40:35

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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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