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Solve each of the definite integrals in Exercises 67–76.

0π/4sin2xcos4xdx.

Short Answer

Expert verified

The answer is13.

Step by step solution

01

Step 1. Given Information.

The integral is0π/4sin2xcos4xdx.

02

Step 2. Explanation.

Simplify the integral using trigonometric identities, tanx=sinxcosxand secx=1cosx.

0π/4tan2xsec2xdx

Substituteu=tanxso, du=sec2xdx

so, limits changes 0 to 1.

role="math" localid="1649243192222" 01u2du.

03

Step 3. Calculation.

Further simplify.

01u2du=u3301=13

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