MATH 2402 Calculus Assignment

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Reference no: EM132483514

MATH 2402 - Calculus II - University of Houston-Downtown

For problems #1-8

Part A. State which initial integration technique could be used for each problem.

There are 4 techniques. You will use each one twice:
• U-Substitution (US)
• Trigonometric Substitution (TS)
• Integration by Parts (IP)
• Partial Fractions (PF)

Part B. Evaluate each problem using the chosen technique. Show all your work neatly and box final answers.

Integration Technique

1. ∫ 1/x²(x-1)² dx

2. ∫ 2x²/√9-x² dx

3. ₀∫¹ xe^-xdx

4. ∫ 2xsec(4x²)dx

5. ∫ 2xcos(6x)dx

6. ∫ 1/x(x²+4) dx

7. ∫3x²+3x+3/(x²+1) dx

8. ∫ 1/x²√4+x² dx

For problems #9-11

A. State a specific reason for why the integral is considered improper.

B. Determine whether the improper integrals diverge or converge. State the value of convergence if converges. Show all your work neatly and box final answers.

9. ₀∫⁸ 3/√8-x dx

10. ₀∫^Π/2 tanθdθ

11. ₃∫^∞1/x(lnx)³dx

Reference no: EM132483514

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