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Estimate cos(x²) dx using (a) the Trapezoidal Rule and (b) the Midpoint Rule, each with n = 4. Give each answer correct to five decimal places. (a) T₁ = (b) M4 (c) By looking at a sketch of the graph of the integrand, determine for each estimate whether it overestimates, underestimates, or is the exact area. ✓1. M4 ? = ? 2. T4 (d) What can you conclude about the true value of the integral? OA. MA cos(x²) dx and M4> f¹ cos(x²) dx OC. T4

Estimate cos(x²) dx using (a) the Trapezoidal Rule and (b) the Midpoint Rule, each with n = 4. Give each answer correct to five decimal places. (a) T₁ = (b) M4 (c) By looking at a sketch of the graph of the integrand, determine for each estimate whether it overestimates, underestimates, or is the exact area. ✓1. M4 ? = ? 2. T4 (d) What can you conclude about the true value of the integral? OA. MA cos(x²) dx and M4> f¹ cos(x²) dx OC. T4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Estimate cos(x²) dx using (a) the Trapezoidal Rule and (b) the Midpoint Rule, each with n = 4. Give each answer correct to five decimal places. (a) T₁ = (b) M4 (c) By looking at a sketch of the graph of the integrand, determine for each estimate whether it overestimates, underestimates, or is the exact area. 1. MA ? ? 2. T4 (d) What can you conclude about the true value of the integral? OA. MA <fo cos(x2) dx < T₁ OB. TA> cos(x²) dx and M4> f¹ cos(x²) dx OC. T4 <fo cos(x²) dx < M₁ OD. TA <fo cos(x²) dx and M4 <fo cos(x²) dx OE. No conclusions can be drawn.
Transcribed Image Text:Estimate cos(x²) dx using (a) the Trapezoidal Rule and (b) the Midpoint Rule, each with n = 4. Give each answer correct to five decimal places. (a) T₁ = (b) M4 (c) By looking at a sketch of the graph of the integrand, determine for each estimate whether it overestimates, underestimates, or is the exact area. 1. MA ? ? 2. T4 (d) What can you conclude about the true value of the integral? OA. MA <fo cos(x2) dx < T₁ OB. TA> cos(x²) dx and M4> f¹ cos(x²) dx OC. T4 <fo cos(x²) dx < M₁ OD. TA <fo cos(x²) dx and M4 <fo cos(x²) dx OE. No conclusions can be drawn.
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