Problem 5: Evaluate $\displaystyle \int \dfrac{(6z - 1) \, dz}{\sqrt{(2z + 1)^3}}$ by Algebraic Substitution
Problem
Evaluate $\displaystyle \int \dfrac{(6z - 1) \, dz}{\sqrt{(2z + 1)^3}}$
Integration
Problem 4: Evaluate $\displaystyle \int \dfrac{y \, dy}{\sqrt[4]{1 + 2y}}$ by Algebraic Substitution
Problem
Evaluate $\displaystyle \int \dfrac{y \, dy}{\sqrt[4]{1 + 2y}}$
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 $\displaystyle \int y^3\sqrt{2y^2 + 1} \,\, dy$
Evaluate the integral of (x dx) / (x^2 + 2) with lower limit of 0 and upper limit of 1
Problem
Evaluate $\displaystyle \int_0^1 \dfrac{x \, dx}{x^2 + 2}$.
| A. 0.2027 | C. 0.2270 |
| B. 0.2207 | D. 0.2072 |
Find the Integral of dx / sqrt(1 + sqrt(x))
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
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
Problem
Integrate $\displaystyle \int \dfrac{dx}{\sqrt[7]{x^2}}$.
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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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