Integral Calculus Spring 2024 Sheet (6) - Integration by Partial Fractions
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Questions and Answers

What is the net area between the curve of 𝑓(𝑥) and the 𝑥-axis in the interval [-3, 7]?

  • 38 sq. units (correct)
  • 24 sq. units
  • 20 sq. units
  • 16 sq. units

What is the total area between the curve of 𝑓(𝑥) and the 𝑥-axis in the interval [-3, 7]?

  • 28 sq. units (correct)
  • 48 sq. units
  • 18 sq. units
  • 30 sq. units

What is the net area between the curve of 𝑓(𝑥) and the 𝑥-axis in the interval [0, 5]?

  • -6 sq. units
  • -10 sq. units
  • 8 sq. units
  • -2 sq. units (correct)

What is the total area between the curve of 𝑓(𝑥) and the 𝑥-axis in the interval [0, 5]?

<p>12 sq. units (C)</p> Signup and view all the answers

What is the integral of ∫(1 + cos 2𝑥) cos2 𝑥 𝑑𝑥?

<p>$\frac{1}{2}x + \frac{1}{4}\sin 4x + C$ (D)</p> Signup and view all the answers

What is ∫ sin4 𝑥 cos2 𝑥 𝑑𝑥 equal to?

<p>$\frac{1}{2}x - \frac{1}{6}\cos 6x + C$ (C)</p> Signup and view all the answers

Evaluate ∫ sec3 2𝑥 cot 2𝑥 1−cos4 𝑥 sin 𝑥 cos5 𝑥 𝑑𝑥.

<p>$-\ln|\cos x| + C$ (C)</p> Signup and view all the answers

What is ∫ tan4 𝑥 sec4 𝑥 tan2 𝑥 𝑑𝑥 equal to?

<p>$\frac{1}{5}\tan^5 x + C$ (B)</p> Signup and view all the answers

What is ∫ cos ln 𝑥 𝑑𝑥?

<p>$xcos(ln(x)) + C$ (D)</p> Signup and view all the answers

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