wk1quiz - f ( x ) = x 3 + x is odd. By a property of the...

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Name: Score: 10B Practice Quiz Please return during Monday’s lecture. You may use whatever resources you like. 1. (5) Approximate the distance, given the following time vs. velocity table. Use n = 3 left endpoint rectangles. t 0 2 4 6 8 10 12 v ( t ) 10 15 17 21 30 32 15 Solution: If we use 3 left endpoint rectangles, then Δ t = b - a 3 = 12 3 = 4 This means our lefthand sum is equal to L ( f ) = 2 X i =0 v ( a + i Δ t t = v ( a t + v ( a + Δ t t + v ( a + 2Δ t t Substituting our values in, we get L ( f ) = 4 v (0) + 4 v (4) + 4 v (8) = 4(10 + 17 + 30) = 228 So the answer is 228 units 2 2. (5) Compute the following definite integral using the fundamental theorem of calculus. Z 1 - 1 ( x 3 + x ) dx Solution: The key thing is that the integrand,
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Unformatted text preview: f ( x ) = x 3 + x is odd. By a property of the denite integral, Z 1-1 ( x 3 + x ) dx = 0 3. (5) Write down, but do not evaluate, an expression for the right hand Riemann sum with n = 100 that approximates Z 2-1 sin( x ) e x dx Solution: Again, the general formula for the righthand Riemann sum is R ( f ) = n-1 X i =1 f ( a + i x ) x In our case, a =-1 and n = 100. This means x = b-a n = 2-(-1) 100 = 3 / 100 Now we can simply plug in our values, obtaining Z 2-1 sin( x ) e x dx L ( f ) = 99 X i =1 sin(-1 + i x ) e-1+ i x x...
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wk1quiz - f ( x ) = x 3 + x is odd. By a property of the...

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