11X1 T14 07 approximations

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<ul><li><p>Approximations To Areas(1) Trapezoidal Rule</p><p>y</p><p>x</p><p>y = f(x)</p><p>a b</p></li><li><p>Approximations To Areas(1) Trapezoidal Rule</p><p>y</p><p>x</p><p>y = f(x)</p><p>a b</p></li><li><p>Approximations To Areas(1) Trapezoidal Rule</p><p>y</p><p>x</p><p>y = f(x)</p><p>a b</p><p> bfafabA 2</p></li><li><p>Approximations To Areas(1) Trapezoidal Rule</p><p>y</p><p>x</p><p>y = f(x)</p><p>a b</p><p>y</p><p>x</p><p>y = f(x)</p><p>a b</p><p> bfafabA 2</p></li><li><p>Approximations To Areas(1) Trapezoidal Rule</p><p>y</p><p>x</p><p>y = f(x)</p><p>a b</p><p>y</p><p>x</p><p>y = f(x)</p><p>a b</p><p> bfafabA 2</p><p>c</p></li><li><p>Approximations To Areas(1) Trapezoidal Rule</p><p>y</p><p>x</p><p>y = f(x)</p><p>a b</p><p>y</p><p>x</p><p>y = f(x)</p><p>a b</p><p> bfafabA 2</p><p>c</p><p> bfcfcbcfafacA 22</p></li><li><p>Approximations To Areas(1) Trapezoidal Rule</p><p>y</p><p>x</p><p>y = f(x)</p><p>a b</p><p>y</p><p>x</p><p>y = f(x)</p><p>a b</p><p> bfafabA 2</p><p>c</p><p> bfcfcbcfafacA 22</p><p> bfcfafac 22</p></li><li><p>yx</p><p>y = f(x)</p><p>a b</p></li><li><p>yx</p><p>y = f(x)</p><p>a bdc</p></li><li><p>yx</p><p>y = f(x)</p><p>a bdc</p><p> bfdfdb</p><p>dfcfcdcfafacA</p><p>2 </p><p>22</p></li><li><p>yx</p><p>y = f(x)</p><p>a bdc</p><p> bfdfdb</p><p>dfcfcdcfafacA</p><p>2 </p><p>22</p><p> bfdfcfafac 222</p></li><li><p>yx</p><p>y = f(x)</p><p>a bdc</p><p> bfdfdb</p><p>dfcfcdcfafacA</p><p>2 </p><p>22</p><p> bfdfcfafac 222</p><p>In general;</p></li><li><p>yx</p><p>y = f(x)</p><p>a bdc</p><p> bfdfdb</p><p>dfcfcdcfafacA</p><p>2 </p><p>22</p><p> bfdfcfafac 222</p><p> ba</p><p>dxxfAreaIn general;</p></li><li><p>yx</p><p>y = f(x)</p><p>a bdc</p><p> bfdfdb</p><p>dfcfcdcfafacA</p><p>2 </p><p>22</p><p> bfdfcfafac 222</p><p> ba</p><p>dxxfArea</p><p> nothers yyyh 22 0</p><p>In general;</p></li><li><p>yx</p><p>y = f(x)</p><p>a bdc</p><p> bfdfdb</p><p>dfcfcdcfafacA</p><p>2 </p><p>22</p><p> bfdfcfafac 222</p><p> ba</p><p>dxxfArea</p><p> nothers yyyh 22 0</p><p>s trapeziumofnumber </p><p> where</p><p>n</p><p>nabh</p><p>In general;</p></li><li><p>yx</p><p>y = f(x)</p><p>a bdc</p><p> bfdfdb</p><p>dfcfcdcfafacA</p><p>2 </p><p>22</p><p> bfdfcfafac 222</p><p>NOTE: there is always one more function value than interval</p><p> ba</p><p>dxxfArea</p><p> nothers yyyh 22 0</p><p>s trapeziumofnumber </p><p> where</p><p>n</p><p>nabh</p><p>In general;</p></li><li><p>e.g.</p><p> points decimal 3 correct to</p><p>2 and 0between ,4 curve under the area</p><p>theestimatetointervals4with RulelTrapezoida theUse</p><p>21</p><p>2 xxxy</p></li><li><p>e.g.</p><p> points decimal 3 correct to</p><p>2 and 0between ,4 curve under the area</p><p>theestimatetointervals4with RulelTrapezoida theUse</p><p>21</p><p>2 xxxy</p><p>5.04</p><p>02</p><p>n</p><p>abh</p></li><li><p>e.g.</p><p> points decimal 3 correct to</p><p>2 and 0between ,4 curve under the area</p><p>theestimatetointervals4with RulelTrapezoida theUse</p><p>21</p><p>2 xxxy</p><p>5.04</p><p>02</p><p>n</p><p>abhx 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p></li><li><p>e.g.</p><p> points decimal 3 correct to</p><p>2 and 0between ,4 curve under the area</p><p>theestimatetointervals4with RulelTrapezoida theUse</p><p>21</p><p>2 xxxy</p><p>5.04</p><p>02</p><p>n</p><p>abh</p><p> nothers yyyh 22Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p></li><li><p>e.g.</p><p> points decimal 3 correct to</p><p>2 and 0between ,4 curve under the area</p><p>theestimatetointervals4with RulelTrapezoida theUse</p><p>21</p><p>2 xxxy</p><p>5.04</p><p>02</p><p>n</p><p>abh</p><p> nothers yyyh 22Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p><p>1 1</p></li><li><p>e.g.</p><p> points decimal 3 correct to</p><p>2 and 0between ,4 curve under the area</p><p>theestimatetointervals4with RulelTrapezoida theUse</p><p>21</p><p>2 xxxy</p><p>5.04</p><p>02</p><p>n</p><p>abh</p><p> nothers yyyh 22Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p><p>1 12 2 2</p></li><li><p>e.g.</p><p> points decimal 3 correct to</p><p>2 and 0between ,4 curve under the area</p><p>theestimatetointervals4with RulelTrapezoida theUse</p><p>21</p><p>2 xxxy</p><p>5.04</p><p>02</p><p>n</p><p>abh</p><p> 2units996.2</p><p>03229.17321.19365.12225.0</p><p> nothers yyyh 22Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p><p>1 12 2 2</p></li><li><p>e.g.</p><p> points decimal 3 correct to</p><p>2 and 0between ,4 curve under the area</p><p>theestimatetointervals4with RulelTrapezoida theUse</p><p>21</p><p>2 xxxy</p><p>5.04</p><p>02</p><p>n</p><p>abh</p><p> 2units996.2</p><p>03229.17321.19365.12225.0</p><p> e exact valu </p><p> nothers yyyh 22Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p><p>1 12 2 2</p></li><li><p>e.g.</p><p> points decimal 3 correct to</p><p>2 and 0between ,4 curve under the area</p><p>theestimatetointervals4with RulelTrapezoida theUse</p><p>21</p><p>2 xxxy</p><p>5.04</p><p>02</p><p>n</p><p>abh</p><p> 2units996.2</p><p>03229.17321.19365.12225.0</p><p> e exact valu </p><p>%6.4</p><p>100142.3</p><p>996.2142.3error %</p><p> nothers yyyh 22Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p><p>1 12 2 2</p></li><li><p>(2) Simpsons Rule</p></li><li><p>(2) Simpsons Rule</p><p> ba</p><p>dxxfArea</p></li><li><p>(2) Simpsons Rule</p><p> ba</p><p>dxxfArea</p><p> nevenodd yyyyh 243 0</p></li><li><p>(2) Simpsons Rule</p><p> ba</p><p>dxxfArea</p><p> nevenodd yyyyh 243 0</p><p>intervalsofnumber </p><p> where</p><p>n</p><p>nabh</p></li><li><p>(2) Simpsons Rule</p><p> ba</p><p>dxxfArea</p><p> nevenodd yyyyh 243 0</p><p>intervalsofnumber </p><p> where</p><p>n</p><p>nabh</p><p>e.g.x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p></li><li><p>(2) Simpsons Rule</p><p> ba</p><p>dxxfArea</p><p> nevenodd yyyyh 243 0</p><p>intervalsofnumber </p><p> where</p><p>n</p><p>nabh</p><p>e.g.</p><p> nevenodd yyyyh 243Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p></li><li><p>(2) Simpsons Rule</p><p> ba</p><p>dxxfArea</p><p> nevenodd yyyyh 243 0</p><p>intervalsofnumber </p><p> where</p><p>n</p><p>nabh</p><p>e.g.</p><p> nevenodd yyyyh 243Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p><p>1 1</p></li><li><p>(2) Simpsons Rule</p><p> ba</p><p>dxxfArea</p><p> nevenodd yyyyh 243 0</p><p>intervalsofnumber </p><p> where</p><p>n</p><p>nabh</p><p>e.g.</p><p> nevenodd yyyyh 243Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p><p>1 14 4</p></li><li><p>(2) Simpsons Rule</p><p> ba</p><p>dxxfArea</p><p> nevenodd yyyyh 243 0</p><p>intervalsofnumber </p><p> where</p><p>n</p><p>nabh</p><p>e.g.</p><p> nevenodd yyyyh 243Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p><p>1 14 2 4</p></li><li><p>(2) Simpsons Rule</p><p> ba</p><p>dxxfArea</p><p> nevenodd yyyyh 243 0</p><p>intervalsofnumber </p><p> where</p><p>n</p><p>nabh</p><p>e.g.</p><p> 2units 084.3</p><p>07321.123229.19365.14235.0</p><p> nevenodd yyyyh 243Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p><p>1 14 2 4</p></li><li><p>(2) Simpsons Rule</p><p> ba</p><p>dxxfArea</p><p> nevenodd yyyyh 243 0</p><p>intervalsofnumber </p><p> where</p><p>n</p><p>nabh</p><p>e.g.</p><p> 2units 084.3</p><p>07321.123229.19365.14235.0</p><p> nevenodd yyyyh 243Area 0x 0 0.5 1 1.5 2y 2 1.9365 1.7321 1.3229 0</p><p>1 14 2 4</p><p>%8.1</p><p>100142.3</p><p>084.3142.3error %</p></li><li><p>Exercise 11I; odds</p><p>Exercise 11J; evens</p><p>Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37</p></li></ul>