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

$ \displaystyle F(x) = \int^0_x \sqrt{1 + \sec t} \,dt $

$$ \biggl[ \textit{Hint:} \int^0_x \sqrt{1 + \sec t} \,dt = - \int^x_0 \sqrt{1 + \sec t} \,dt \biggr] $$

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00:44

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Campbell University

Oregon State University

Harvey Mudd College

Idaho State University

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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01:21

Use the Second Fundamental…

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Use the Fundamental Theore…

using the fundamental damn of calculus. We know we have negative D over DX, given the head and the problem from the bounds of pied acts scored of one plus seeking T d t Now for a final solution. We know the teas go away, are placed with access, so we have squirt of one plus seeking X on the negatives on the outside.

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