CPM Homework Help : APCALC Problem 7-146

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7-146.

Evaluate each of the following integrals.

$\int _ { 0 } ^ { 1 / 6 } \frac { 1 } { \sqrt { 1 - 9 x ^ { 2 } } } d x$
Hint (a):
$\int_{0}^{\frac{1}{6}}\frac{1}{\sqrt{1-(3x)^{2}}}dx$
What trig derivative do you recognize?

$\int _ { 0 } ^ { \sqrt { 3 } / 2 } \frac { 1 } { 1 + 4 x ^ { 2 } } d x$
Hint (b):
Refer to the hint in part (a).
Also, remember that $4x^2 = (2x)^2$ .

$\int _ { 0 } ^ { 1 } 2 ^ { 3 x } d x$
Answer (c):
$=\frac{1}{3\ln(2)}2^{3x}\Big|_0^1=\frac{7}{3\ln(2)}$

$\int _ { 0 } ^ { 1 } e ^ { 5 x } d x$
Hint (d):
This integral is very much like that in part (c).

Compute without a calculator

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