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Set Up, but Do Not Evaluate, an Integral for the Length

Question 5

Multiple Choice

Set up, but do not evaluate, an integral for the length of the curve.
y=6exsinx,0x9π2y = 6 e ^ { x } \sin x , \quad 0 \leq x \leq \frac { 9 \pi } { 2 }


A)
L=09x/2136e2x(1+sin2x) dxL = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 - 36 e ^ { 2 x } ( 1 + \sin 2 x ) } d x
B)
L=09x/21+36e2x(1+sin2x) dxL = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 + 36 e ^ { 2 x } ( 1 + \sin 2 x ) } d x
C)
L=09x/2136e2x(1sin2x) dxL = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 - 36 e ^ { 2 x } ( 1 - \sin 2 x ) } d x
D)
L=09x/21+36e2x(1sin2x) dxL = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 + 36 e ^ { 2 x } ( 1 - \sin 2 x ) } d x
E)
L=09x/21+36e2x(1sinx) dxL = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 + 36 e ^ { 2 x } ( 1 - \sin x ) } d x

Correct Answer:

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