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Which of the integrals $ \displaystyle \int^{0.5}_0 \cos (x^2) \,dx $, $ \displaystyle \int^{0.5}_0 \cos \sqrt{x} \,dx $ is larger? Why?
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00:52
Frank Lin
Calculus 1 / AB
Chapter 5
Integrals
Section 2
The Definite Integral
Integration
Missouri State University
Harvey Mudd College
Baylor University
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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01:19
Okay, we know that from 0.5, this court of X has to be greater than or equal to x squared. Therefore, we know that because co sign X is decreasing from 0.5, you know that co sign squared of acts has to be less than or equal to co sign of X squared. Therefore, we know that the integral from 0.5 co sign X squared d X has to be very correlates to this.
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