# integration

**Problem**

Evaluate $\displaystyle \int_0^1 \dfrac{x \, dx}{x^2 + 2}$.

A. 0.2027 | C. 0.2270 |

B. 0.2207 | D. 0.2072 |

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**Problem**

Evaluate $\displaystyle \int_0^9 \dfrac{1}{\sqrt{1 + \sqrt{x}}}$

A. 4.667 | C. 5.333 |

B. 3.227 | D. 6.333 |

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## Perimeter of the curve r = 4(1 + sin theta) by integration

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## Example 03 | The General Power Formula

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## Example 02 | The General Power Formula

**Problem**

Evaluate $\displaystyle \int \sqrt{ax + b} ~ dx$.

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## Example 01 | The General Power Formula

**Problem**

Evaluate $\displaystyle \int \left( \sqrt{x} + x\sqrt{x} + \dfrac{1}{\sqrt{x}} \right) \, dx$

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## 4 - 6 Examples | Indefinite Integrals

Evaluate the following:

**Example 4:** $\displaystyle \int \sqrt{x^3 + 2} \,\, x^2 \, dx$

**Example 5:** $\displaystyle \int \dfrac{(3x^2 + 1) \, dx}{\root 3\of {(2x^3 + 2x + 1)^2}}$

**Example 6:** $\displaystyle \int (1 - 2x^2)^3 \, dx$

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## 1 - 3 Examples | Indefinite Integrals

Evaluate the following integrals:

**Example 1:** $\displaystyle \int \dfrac{2x^3+5x^2-4}{x^2}dx$

**Example 2:** $\displaystyle \int (x^4 - 5x^2 - 6x)^4 (4x^3 - 10x - 6) \, dx$

**Example 3:** $\displaystyle \int (1 + y)y^{1/2} \, dy$

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