a$.$ Write and simplify the integral that gives the arc length of the following curve on the given integral.

b$.$ If$$ necessary, use a calculator to evaluate the approximate integral.

yequals$=$cosine $3$ xcos$3$x$,$

for

$00$less than or equals$$xless than or equals$$pi

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Part $1$

a$.$ Which of the following is a simplified form of the$$ integral?

A$.$Integral from $0$ to pi StartRoot $1$ plus $9$ cosine squared $3$ x EndRoot dx

Integral from $0$ to pi StartRoot $1$ plus $9$ cosine squared $3$ x EndRoot dx$0$$1+9$cos$23$xdx

B$.$Integral from $0$ to pi StartRoot $1$ plus $3$ sine squared $3$ x EndRoot dx

Integral from $0$ to pi StartRoot $1$ plus $3$ sine squared $3$ x EndRoot dx$0$$1+3$sin$23$xdx

C$.$Integral from $0$ to pi StartRoot $1$ plus $9$ sine squared $3$ x EndRoot dx

Integral from $0$ to pi StartRoot $1$ plus $9$ sine squared $3$ x EndRoot dx$0$$1+9$sin$23$xdx

Your answer is correct.

D$.$Integral from $0$ to pi minus $3$ cosine $3$ x dx

Integral from $0$ to pi minus $3$ cosine $3$ x dx$0$$3$cos$3$x$$dx

Part $2$