Chapter 6: Q. 13 (page 510)

For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals
$π \int_{0}^{\frac{π}{2}} \cos^{2} (x) d x a n d π \int_{\frac{π}{2}}^{π} \cos^{2} (x) d x$

Short Answer

Expert verified

Both integrals are equal

Step by step solution

Given information

We are given two integrals $π \int_{0}^{\frac{π}{2}} \cos^{2} (x) d x a n d π \int_{\frac{π}{2}}^{π} \cos^{2} (x) d x$

Explaination

We will substitute $\cos (x^{2}) = \frac{1 - \cos 2 x}{2}$

Hence the integral becomes

$π \int_{0}^{\frac{π}{2}} \frac{1 - \cos 2 x}{2} d x a n d π \int_{\frac{π}{2}}^{π} \frac{1 - \cos 2 x}{2} d x$

On integrating we will get sine terms

And after substituting the limits we will get equal values

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals
$π \int_{0}^{\frac{π}{2}} \cos^{2} (x) d x a n d π \int_{\frac{π}{2}}^{π} \cos^{2} (x) d x$

Short Answer

Step by step solution

Given information

Explaination

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Decision Maths

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integralsπ∫0π2cos2xdxandπ∫π2πcos2xdx

Short Answer

Step by step solution

Given information

Explaination

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Decision Maths

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals
$π \int_{0}^{\frac{π}{2}} \cos^{2} (x) d x a n d π \int_{\frac{π}{2}}^{π} \cos^{2} (x) d x$