Home > APCALC > Chapter 8 > Lesson 8.2.1 > Problem8-70

8-70.

Multiple Choice: Evaluate $\int _ { 1 } ^ { 2 } \frac { 2 } { x ^ { 2 } } d x$ without a calculator.

1. $2 \ln(2)$

1. $2 \ln(4)$

1. $-\frac { 1 } { 3 }$

1. $\frac { 1 } { 3 }$

1. $1$

TWO of these multiple choice options should be eliminated immediately!

$\text{After all, only the family of }y=\frac{1}{x}\text{ has antiderivatives that involve the natural logarithm. }$

$y=\frac{1}{x^{2}}, \ y=\frac{1}{x^{3}}, \ y=\frac{1}{x^{4}}, \text{ etc. can be anti-differentiated by 'undoing' the Power Rule. }$