Question

Using the substitution $u = \sin(2x)$, $\int_{\pi/6}^{\pi/2} \sin^5(2x)\cos(2x)\,dx$ is equivalent to A. $-2 \int_{1/2}^1 u^5 \,du$ B. $\frac{1}{2} \int_{1/2}^1 u^5 \,du$ C. $\frac{1}{2} \int_0^{\sqrt{3}/2} u^5 \,du$ D. $\frac{1}{2} \int_{\sqrt{3}/2}^0 u^5 \,du$ E. $2 \int_{\sqrt{3}/2}^0 u^5 \,du$

          Using the substitution $u = \sin(2x)$, $\int_{\pi/6}^{\pi/2} \sin^5(2x)\cos(2x)\,dx$ is equivalent to
A. $-2 \int_{1/2}^1 u^5 \,du$
B. $\frac{1}{2} \int_{1/2}^1 u^5 \,du$
C. $\frac{1}{2} \int_0^{\sqrt{3}/2} u^5 \,du$
D. $\frac{1}{2} \int_{\sqrt{3}/2}^0 u^5 \,du$
E. $2 \int_{\sqrt{3}/2}^0 u^5 \,du$

Using the substitution u = sin(2x), ∫π/6^π/2sin^5(2x)cos(2x) dx is equivalent to
A. -2 ∫1/2^1 u^5 du
B. (1)/(2)∫1/2^1 u^5 du
C. (1)/(2)∫0^√(3)/2 u^5 du
D. (1)/(2)∫√(3)/2^0 u^5 du
E. 2 ∫√(3)/2^0 u^5 du

Added by Ryan M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hoan Nguyen

Step 1

Then du/dx = 2 cos(2x), so du = 2 cos(2x) dx and therefore cos(2x) dx = (1/2) du. Show more…

Show all steps

Thanks for your feedback!

Using the substitution u=sin(2x),int_((pi )/(6))^((pi )/(2)) sin^(5)(2x)cos(2x)dx is equivalent to -2int_((1)/(2))^1 u^(5)du (1)/(2)int_((1)/(2))^1 u^(5)du (1)/(2)int_0^((sqrt(3))/(2)) u^(5)du (1)/(2)int_((sqrt(3))/(2))^0 u^(5)du 2int_((sqrt(3))/(2))^0 u^(5)du Using the substitution u-sin2x sin2cos2dxis equivalent to u du 1/2 A 12 us du J1/2 ? CV3/2 1 udu 2 c 12 us du V3/2 E us du V3/2