EBUS CAL12 Chapter 5 Integration Test-1

Step 1: Compute \(\Delta x=2.5\). Step 2: Use right endpoints. Step 3: Sum heights and multiply by \(\Delta x\). Answer: 468.75

Step 1: Apply linearity. Step 2: Compute \(3-5(-5)=28\). Answer: 28

Step 1: Split at \(x=5\). Step 2: Add both positive areas. Answer: 65

Step 1: Apply FTC. Answer: True

Step 1: Combine integrals. Step 2: Evaluate on \([1,2]\). Step 3: Round to three decimals. Answer: 24.426

Step 1: Split at x-intercepts. Step 2: Add absolute areas. Answer: True

Step 1: Let \(u=\cos x\). Step 2: Integrate. Answer: \(-\frac{\cos^7x}{7}+C\)

Step 1: Simplify first. Step 2: Integrate termwise. Answer: False

Step 1: Integrate each term. Answer: \(-\frac{5}{2x^2}+\frac34e^{4x}+C\)

Step 1: Integrand is odd. Step 2: Symmetric interval. Answer: True