Integration

Problem 4: Integral of (y dy) / 4th root(1 + 2y) by Algebraic Substitution

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

Answer Key

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)

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

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

cardioid-pointing-upward.jpg

 

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