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Pre-Calc Homework Solutions 208

Pre-Calc Homework Solutions 208 - wide as in E p sin x dx 2...

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Section 5.2 Definite Integrals (pp. 258–268) Exploration 1 Finding Integrals by Signed Areas 1. 2 2. (This is the same area as E p 0 sin x dx , but below the x -axis.) [ 2 2 p , 2 p ] by [ 2 3, 3] 2. 0. (The equal areas above and below the x -axis sum to zero.) [ 2 2 p , 2 p ] by [ 2 3, 3] 3. 1. (This is half the area of E p 0 sin x dx .) [ 2 2 p , 2 p ] by [ 2 3, 3] 4. 2 p 1 2. (The same area as E p 0 sin x dx sits above a rectangle of area p 3 2.) [ 2 2 p , 2 p ] by [ 2 3, 3] 5. 4. (Each rectangle in a typical Riemann sum is twice as tall as in E p 0 sin x dx .) [ 2 2 p , 2 p ] by [ 2 3, 3] 6. 2. (This is the same region as in E p 0 sin x dx , translated 2 units to the right.) [ 2 2 p , 2 p ] by [ 2 3, 3] 7. 0. (The equal areas above and below the x -axis sum to zero.) [ 2 2 p , 2 p ] by [ 2 3, 3] 8. 4. (Each rectangle in a typical Riemann sum is twice as
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Unformatted text preview: wide as in E p sin x dx .) [ 2 2 p , 2 p ] by [ 2 3, 3] 9. 0. (The equal areas above and below the x-axis sum to zero.) [ 2 2 p , 2 p ] by [ 2 3, 3] 10. 0. (The equal areas above and below the x-axis sum to zero, since sin x is an odd function.) [ 2 2 p , 2 p ] by [ 2 3, 3] Exploration 2 More Discontinuous Integrands 1. The function has a removable discontinuity at x 5 2. [ 2 4.7, 4.7] by [ 2 1.1, 5.1] 2. The thin strip above x 5 2 has zero area, so the area under the curve is the same as E 3 ( x 1 2) dx , which is 10.5. [ 2 4.7, 4.7] by [ 2 1.1, 5.1] 208 Section 5.2...
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