MAT237Y1 Lecture Notes - Antiderivative, Even And Odd Functions, Special Functions
Document Summary
This theorem is so important it had to be split up into two parts. This says the area under any (continuous) curve is f (b) f (a). In other words, just plug in the end points and subtract and you have the area. Finally, we"re o of solving for the area under a curve and getting back a functionwe now get actual numbers for the area. For notation purposes, i"ll be writing this also as it means the same thing as f (b) f (a). You might also see in the book this notation: Remember, x is a variable here, while a and b are constants. 4 2x dx = 4x x2(cid:12)(cid:12)(cid:12)3. = 4(3) 32 [4( 1) ( 1)2] = 12 9 [ 5] = 8. So, the idea here is that you antidi erentiate exactly as you would in 6. 2 and then plug in the two numbers to get out the actual area.
