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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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01:12

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Missouri State University

Campbell University

Oregon State University

Boston College

Lectures

05:53

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.

40:35

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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Use Part 1 of the Fundamen…

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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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