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Question

Let ∣ ∣ ∣2cos2xsin(2x)sinxsin(2x)2sin2xcosxsinxcosx0∣ ∣ ∣

Find 1ππ/20[f(x)+f(x)]dx

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Solution

We have, f(x)=∣ ∣ ∣2cos2xsin(2x)sinxsin(2x)2sin2xcosxsinxcosx0∣ ∣ ∣

applyingC1C12sinxC3andC2C2+2cosxC3wegetf(x)=∣ ∣20sinx02cosxsinxcosx0∣ ∣

f(x)=2sin2x+2cos2x=2f(x)=0

1ππ/20[f(x)+f(x)]dx=1ππ/202dx

f(x)=1π2(π2)=1

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