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Show that $ \displaystyle \int_0^\infty e^{-x^2}\ dx = \displaystyle \int_0^1 \sqrt{-\ln y}\ dy $ by interpreting the integrals as areas.

$\int_{0}^{\infty} e^{-x^{2}} d x=\int_{0}^{1} \sqrt{-\ln y} d y$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

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Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

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Show that $ \displaystyle …

Show that $$\int_{0}^{\inf…

03:31

Show that $\int_{0}^{1} …

01:04

Evaluate the integral, giv…

03:50

01:33

02:07

Evaluate the integrals.

02:26

Make the $u$ -substitution…

03:30

Evaluate the integrals tha…

01:20

Evaluate the integral by i…

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In mathematics, integration is one of the two main operations in calculus, w…

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Show that $ \displaystyle \int_0^\infty x^2 e^{-x^2}\ dx = \frac{1}{2} \disp…

Show that $$\int_{0}^{\infty} x^{2} e^{-x^{2}} d x=\frac{1}{2} \int_{0}^{\in…

Show that $\int_{0}^{1} \int_{0}^{2 x} x^{2} d y d x \neq \int_{0}^{2} \in…

Evaluate the integral, given that$\int_{0}^{\infty} e^{-x^{2}} d x=\frac…

Evaluate the integrals.$$\int \frac{d x}{\sqrt{1-e^{2 x}}} \quad(x&l…

Make the $u$ -substitution and evaluate the resulting definite integral.…

Evaluate the integrals that converge.$$\int_{0}^{+\infty} x e^{-x^{2…

Evaluate the integral by interpreting it in terms of areas.

$ \disp…