Mat 231 WA5.docx - Name College ID Thomas Edison State...

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Name: 1. Find the general antiderivative. 2 cos 4 sin x dx x = cos 4 sin x x . 1 sin x = 4 cot csc x x = 4csc x c 2. Find the general antiderivative. (4 2 ) x x e dx 1 1 2 4 2 4 2 2 2 1 1 x x x d d x x e e c x e c dx dx 3. Find the general antiderivative. 2 3 4 4 dx x 1 2 3 1 3 tan 4 1 4 dx x c x WA 5, p. 1
4. Determine the position function if the velocity function is ( ) 3 2 t v t e and the initial position is (0) 0 s . ( ) ( ) s t v t dt => (3 2) 3 2 t t e dt e t c => ( ) 3 2 t s t e t c 0 (0) 3 2(0) 3 s e c c   Position function ( ) 3 2 3 t s t e t 5. Write out all terms and compute the sums. 6. Use summation rules to compute the sum. 140 2 1 ( 2 4) n n n = 140 140 140 2 1 1 1 ( 1)(2 1) ( 1) ( ) 2 4 4 6 2 n n n n n n n n n n n => = 140(141)(281) 140(141) 4(140) 943,670 6 2 WA 5, p. 2
7. Approximate the area under the curve on the given interval using n rectangles and the evaluation rules (a) left endpoint, (b) midpoint, and (c) right endpoint. 2 1 y x on [0, 2], n = 16 2 0 2 b a x n n n 2 i i x n 1 2( 1) i i x n 1 ( ) n n i i A A f c x a. Left side endpoint 1 2( 1) i i i c x n 2 1 2 2( 1) ( ) 1 n i i A n n = 2 2 2 2 2 1 2 4( 2 1 2 4 ( 1)(2 1) 8 ( 1) 4 1 ( ) ( ) 1( ) 6 2 n i i i n n n n n n n n n n n n n => 2 2 2 1 4 16(17)(33) 8 16(17) 4 ( ) ( ) (16) 16 8 16 6 16 2 16 1 187 17 1 2249 16 4.392 8 8 4 64 512 b.) midpoint 1 1 ( ) 2 i i i c x x 1 2( 1) 2 2 1 ( ) 2 i i i i c n n n 2 1 1 2 2 1 ( ) ( ) 1 n n i i i i i A A f c x n n = 2 2 2 2 2 1 2 4 4 1 2 4 ( 1)(2 1) 4 ( 1) 1 1 ( ) ( ) 1 6 2 n i i i n n n n n n n n n n n n

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