Determine the integral by making an appropriate substitution.
-$\int 12 \sin x \sqrt { \cos x }$ dx
A) 18 $( \cos x ) ^ { 3 / 2 }$ + C
B) 8 $( \cos x ) ^ { 3 / 2 }$ + C
C) -18 $( \cos x ) ^ { 3 / 2 }$ + C
D) -8 $( \cos x ) ^ { 3 / 2 }$ + C

Question

Determine the integral by making an appropriate substitution. 
-$\int 12 \sin x \sqrt { \cos x }$ dx
A) 18 $( \cos x ) ^ { 3 / 2 }$ + C
B) 8 $( \cos x ) ^ { 3 / 2 }$ + C
C) -18 $( \cos x ) ^ { 3 / 2 }$ + C
D) -8 $( \cos x ) ^ { 3 / 2 }$ + C

Quizplus · Accepted Answer

Using the substitution $ u = \cos x $, $ du = -\sin x \, dx $. The integral becomes $-12 \int \sqrt{u} \, du$, which evaluates to $-8 u^{3/2} + C$. Substituting back $ u = \cos x $, we get $-8 (\cos x)^{3/2} + C$.

Determine the Integral by Making an Appropriate Substitution ∫12sin⁡xcos⁡x\int 12 \sin x \sqrt { \cos x }∫12sinxcosx​

Determine the Integral by Making an Appropriate Substitution $\int 12 \sin x \sqrt { \cos x }$