### Home > APCALC > Chapter 7 > Lesson 7.3.4 > Problem7-146

7-146.

Evaluate each of the following integrals.

1. $\int _ { 0 } ^ { 1 / 6 } \frac { 1 } { \sqrt { 1 - 9 x ^ { 2 } } } d x$

$\int_{0}^{\frac{1}{6}}\frac{1}{\sqrt{1-(3x)^{2}}}dx$

What trig derivative do you recognize?

1.  $\int _ { 0 } ^ { \sqrt { 3 } / 2 } \frac { 1 } { 1 + 4 x ^ { 2 } } d x$

Refer to the hint in part (a).
Also, remember that $4x^2 = (2x)^2$.

1. $\int _ { 0 } ^ { 1 } 2 ^ { 3 x } d x$

$=\frac{1}{3\ln(2)}2^{3x}\Big|_0^1=\frac{7}{3\ln(2)}$

1. $\int _ { 0 } ^ { 1 } e ^ { 5 x } d x$

This integral is very much like that in part (c).