   Chapter 4.5, Problem 35E

Chapter
Section
Textbook Problem

# Evaluate the definite integral. ∫ 0 1 cos ( π t / 2 ) d t

To determine

To evaluate:

The given definite integral 01cosπt2dt.

Explanation

1) Concept:

i) The substitution rule for definite integral:

If g'(x) is a continuous function on a,b whose f is continuous on range of u=g(x), then abfgxg'(x)dx=g(a)g(b)f(u)du.

ii)

abcfxdx=cabfxdx

2) Given:

01cosπt2dt

3) Calculation:

The given integral is

01cosπt2dt. Here, use the substitution method.

Substitute πt2=u

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Expand each expression in Exercises 122. (x+yxy)2

Finite Mathematics and Applied Calculus (MindTap Course List)

#### What are the two requirements for a random sample?

Statistics for The Behavioral Sciences (MindTap Course List)

#### The appropriate option for the value of (123).

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th 