Multivariable calculus, class #16: Double integrals

Mathematician spotlight: Erik Demaine

We teach how to do the magic trick of cutting out a 5-pointed star with a single cut. We review single-variable integrals (to find area) and introduce multivariable integrals (to find volume, etc.). We do some examples of double integrals that can be computed using basic geometry. We then compute them algebraically, in both orders of integration. We explain what a double integral means, where the inner integral is the area of a slice, and the outer integral adds up the volumes of those slices, with a tiny thickness. Finally, we discuss Fubini's Theorem that you can switch the order of integration, and do an example that is impossible in one order and easy in the other.

[RajatKumar-uxjg]

Please make video on some more chapter . Your lectures is amazing and it really helps a lot..

[brijeshkumar-ujgo]

Mam thanks for making maths interesting.I really praise your hardwork and I can assure you that it was realy helpful to many of us.

[romitabiswas]

thank you ma'am. That was really helpful

[Gamma_Digamma]

Antiderivative of sin(x^2)...
It's non elementary, dear Watson