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Integration

Problem 5: Evaluate $\displaystyle \int \dfrac{(6z - 1) \, dz}{\sqrt{(2z + 1)^3}}$ by Algebraic Substitution

Problem
Evaluate $\displaystyle \int \dfrac{(6z - 1) \, dz}{\sqrt{(2z + 1)^3}}$

Problem 4: Evaluate $\displaystyle \int \dfrac{y \, dy}{\sqrt[4]{1 + 2y}}$ by Algebraic Substitution

Problem 3: Evaluate $\displaystyle \int \dfrac{x^3 \, dx}{(x^2 + 1)^3}$ by Algebraic Substitution

Problem
Evaluate $\displaystyle \int \dfrac{x^3 \, dx}{(x^2 + 1)^3}$

Problem 2: Evaluate $\displaystyle \int y^3\sqrt{2y^2 + 1} \,\, dy$ by Algebraic Substitution

Problem
Evaluate $\displaystyle \int y^3\sqrt{2y^2 + 1} \,\, dy$

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

A. 0.2027	C. 0.2270
B. 0.2207	D. 0.2072

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

A. 4.667	C. 5.333
B. 3.227	D. 6.333

Using Simpson’s One-third Rule for Integration Problems (Tagalog)

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

Problem
What is the perimeter of the curve r = 4(1 + sin θ)?

The answer is 32 units. For detailed solution, follow the link by clicking on the figure.

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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