Calculus #8: Is $\int { x \quad dx } = \frac{x^{2}}{2}$ ?

Calculus Level 1

True or False?

$\large \int { x \quad dx } = \frac{x^{2}}{2}$

Note: If there is a small mistake, click $\boxed{False}$ .

False True

2 solutions

Munem Shahriar
Oct 2, 2017

$\int xdx$

$= \dfrac{x^{1+1}}{1+1} +C$

$= \dfrac{x^2}{2} + C$

Hence the statement is $\color{#D61F06} \boxed{\text{false}}$

How to write red-colored boxed messages?

. . - 3 months, 3 weeks ago

(You need to add the C to the first 2 terms. It doesn't magically appear...)

Ron Lauterbach - 3 years, 8 months ago

Ron Lauterbach
Oct 2, 2017

This would be the correct version:

$\large \int { x \quad dx } = \frac{x^{2}}{2} + C$