Indefinite Integrals: Substitution Rule

March 5, 2008

Evaluate the following integrals:

  1. \displaystyle \int \frac{x^3}{\sqrt{x^2 + 25}}\ dx
  2. \displaystyle \int \tan^2 \theta \sec^4 \theta\ d \theta
  3. \displaystyle \int \sqrt[3]{x^2 - 2x + 1}\ dx

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Posted by Tina

Derivatives of Integrals

March 5, 2008

Evaluate the following.

  1. \displaystyle \frac{d}{dx} \int_{x}^{0} \sqrt{1+t^{4}}\ dt
  2. \displaystyle \frac{d}{dx} \int_{\frac{1}{x}}^{\sqrt{x}} \cos t^{2}\ dt,\; x>0
  3. \displaystyle \frac{d^{2}}{dx^{2}} \int_{0}^{x} \left( \int_{1}^{\sin t} \sqrt{1+u^{4}}\ du \right) dt

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Posted by wMw