Brilliant

Practice

Algebra
Geometry
Number Theory
Calculus
Discrete Mathematics
Basic Mathematics
Logic
Classical Mechanics
Electricity and Magnetism
Computer Science
Quantitative Finance
Chemistry

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Log in with Facebook Log in with Google

or

Log in with email

Join using Facebook Join using Google

or

Join using email

New user? Sign up

Existing user? Log in

Definitely not a semicircle

Calculus Level 3

$1-(1-x)^{1-x}x^x$ The curve looks like a semicircle with a radius 0.5.

Which is larger, $\displaystyle\int_0^1 1-(1-x)^{1-x}x^x dx$ or $\dfrac{\pi}8$ ?

\displaystyle\int_0^1 1-(1-x)^{1-x}x^x dx

Can't determine.

\dfrac{\pi}8

View solutions

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable. Find out if you're right!

Sign up to access problem solutions.

That seems reasonable. Find out if you're right!

Log in with Facebook Log in with Google

or

Log in with email

Join using Facebook Join using Google

or

Join using email

New user? Sign up

Existing user? Log in

by X X

×

Problem Loading...

Note Loading...

Set Loading...