In Exercises 45 and 46, use the inverse matrix found in Exercise 19 to solve the system of linear equations. x y z 03x 5y 4z 53x 6y 5z 2

Math241 Lecture 7: Double Integrals Just like how in single variable calculus the integral could be interpreted as the area under a curve, in multivariable calculus the double integral can be interpreted as the volume under a surface. ❑ volume= f x,y dA ∬R ( ) R is the region in which you are integrating. Area is the derivative of volume. Iterated Integrals Now the easiest type of double integral is integrating over a rectangle. That is, we are integrating over a fixed surface that is constant. First we take the inner integral and integrate with respect to that variable while holding the other one constant. Then we integrate the outer variable like we did in Calculus 1. ❑ 1. ∬ 5x+ydydx [2,5] x