Indefinitely definite!

Calculus Level 1

Which of these is greater? $\large \int_0^1 2^{x^2}\, dx \text{ or } \int_0^1 2^{x^3}\,dx\quad ?$

\int_0^1 2^{x^2}\, dx

\int_0^1 2^{x^3}\, dx

Both are equal

3 solutions

J D
May 10, 2016

Because $x^2$ is greater than $x^3$ on $(0,1)$ , exponentiating both sides means that $2^{x^2}$ is greater than $2^{x^3}$ , so there is more area under the curve of $2^{x^2}$ (integral of $2^{x^2}$ is greater).

That's really cool!

Kishore S. Shenoy - 5 years, 1 month ago

This was my train of thought too :)

Michael Fuller - 5 years ago

Amarildo Aliaj
Nov 1, 2016

Hana Wehbi
May 11, 2016

evalf(int(2^(x^2),x=0..1));

                         1.288226364

evalf(int(2^(x^3),x=0..1));

                         1.213987326

using Maple.

Indefinitely definite!

3 solutions

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