cos y S- = dy V1+ sin y

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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How would I solve this integral?

The integral shown in the image is:

\[
\int \frac{\cos y}{\sqrt{1 + \sin^2 y}} \, dy
\]

This mathematical expression represents the integration of the function \(\frac{\cos y}{\sqrt{1 + \sin^2 y}}\) with respect to \(y\). It involves trigonometric and radical components. This type of integral can arise in calculus when dealing with trigonometric substitution or integration techniques involving square roots of sums of squares.
Transcribed Image Text:The integral shown in the image is: \[ \int \frac{\cos y}{\sqrt{1 + \sin^2 y}} \, dy \] This mathematical expression represents the integration of the function \(\frac{\cos y}{\sqrt{1 + \sin^2 y}}\) with respect to \(y\). It involves trigonometric and radical components. This type of integral can arise in calculus when dealing with trigonometric substitution or integration techniques involving square roots of sums of squares.
Expert Solution
Step 1

Given,

cosy1+sin2ydy

Now assuming ,   t = siny

then dt/dy = cosy

dt =cosydy

Sustituting the values of t and dt in the integral 

dt1+t2

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