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Question 6 [13 marks] a) Suppose we know that water is flowing into a pool at a rate f(t)=x?(x³+1) liters per hours. Use Simpson's 1/3 Rule to estimate the total amount of water flows into the pool in the first two hours, ?[0 to 2] f(t) dt with h=0.5 in 3 decimal points. (5 marks) b) Use the Romberg integration to find the approximation for the shaded area under the curve with f(x)=4x³-16x as shown in Figure 1 until |R_{i,j} - R_{i,j-1}| < 0.05. Do the calculations in 2 decimal points. (8 marks) Figure 1

          Question 6 [13 marks]
a) Suppose we know that water is flowing into a pool at a rate f(t)=x?(x³+1) liters per hours. Use Simpson's 1/3 Rule to estimate the total amount of water flows into the pool in the first two hours, ?[0 to 2] f(t) dt with h=0.5 in 3 decimal points. (5 marks)
b) Use the Romberg integration to find the approximation for the shaded area under the curve with f(x)=4x³-16x as shown in Figure 1 until |R_{i,j} - R_{i,j-1}| < 0.05. Do the calculations in 2 decimal points. (8 marks)
Figure 1

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Question 6 [13 marks]
a) Suppose we know that water is flowing into a pool at a rate f(t)=x?(x³+1) liters per hours. Use Simpson's 1/3 Rule to estimate the total amount of water flows into the pool in the first two hours, ?[0 to 2] f(t) dt with h=0.5 in 3 decimal points. (5 marks)
b) Use the Romberg integration to find the approximation for the shaded area under the curve with f(x)=4x³-16x as shown in Figure 1 until |Ri,j - Ri,j-1| < 0.05. Do the calculations in 2 decimal points. (8 marks)
Figure 1

Added by Amanda B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur B

02/14/2022

Step 1

Given: - Water flow rate into pool K: xvx^3 + liters per hour - Rate of flow: xvx^3 - Time: 2 hours Using Simpson's 1/3 Rule formula: ∫[0,2] (xvx^3) dx ≈ (0.5/3) [f(0) + 4f(0.5) + 2f(1) + 4f(1.5) + f(2)] Now, calculate the values of f(0), f(0.5), f(1), f(1.5), Show more…

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Suppose we know that water is flowing into a pool at a rate f(t)=x√(x³+1) liters per hours. Use Simpson's 1/3 Rule to estimate the total amount of water flows into the pool in the first two hours, ∫[0 to 2] f(t) dt with h=0.5 in 3 decimal points. Use the Romberg integration to find the approximation for the shaded area under the curve with f(x)=4x³-16x as shown in Figure 1 until |R_{i,j} - R_{i,j-1}| < 0.05. Do the calculations in 2 decimal points.

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