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Find the value of \int \sin ^{2}x \cos ^{2} x dx 

  • Option 1)

    x/2-\frac{\sin 2x}{2}+C

  • Option 2)

    x/4-\frac{\sin 4x}{4}+C

  • Option 3)

    x/4-\frac{\sin 4x}{16}+C

  • Option 4)

    x/2-\frac{\sin 2x}{4}+C

 

Answers (1)

best_answer

As we have learned

Integration of trigonometric function of power m -

\int sin^{m}xdx    and 

 \int cos^{m}xdx

- wherein

for m=2,

sin^{2}x=\frac{1-cos 2x}{2}

for m=3,

sin3x=3sinx-4sin^{3}x

 

 

=1/4\int (\sin 2x)^{2}dx= \int (\frac{1- \cos 4x}{4})dx

= x/4 -\frac{\sin 4x}{16} +C


Option 1)

x/2-\frac{\sin 2x}{2}+C

This is incorrect

Option 2)

x/4-\frac{\sin 4x}{4}+C

This is incorrect

Option 3)

x/4-\frac{\sin 4x}{16}+C

This is correct

Option 4)

x/2-\frac{\sin 2x}{4}+C

This is incorrect

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prateek

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