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Fundamental theorem of calculusGiven any antiderivative F the area under the curve between a and b is given by the definite integral( )( )( )baf x dxF bF a=−∫Why is this true?Area(a,b+h) - Area(a,b) f(b) h soArea(a,b+h) - Area(a,b)( )hf b≈→Problem30Find (82 )x dx+∫Area under f(x) = 8 + 2x from a=0 to b=3302(82 ) (3)(0)( )8(3)24933 (0)0Area = (3)(0)33xdxFFF xxxFFFF+=−=+=+==−=∫Area under f(x) = 8 + 2x from a=0 to b=31212Trapezoid with height 3, 8, 14814Area 33322hbbbbh===++===81403Porsche 928, p. 415The velocity at tseconds is10t – t2/4for t ≤20 secondsHow far does the car move during this time?1 mile per hour ≈½ yard per second02040608010005101520
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