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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?

$\int_{0}^{0.5} \cos x^{2} d x$ is bigger

00:29

Amrita B.

Calculus 1 / AB

Chapter 5

Integrals

Section 2

The Definite Integral

Integration

Campbell University

Baylor University

University of Michigan - Ann Arbor

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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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