Verify by differentiation that the formula is correct. Integral \cos^{2}xdx=1/2x+1/4\sin

embaseclielenzn

embaseclielenzn

Answered question

2021-12-06

Verify by differentiation that the formula is correct. Integral cos2xdx=12x+14sin2x+C

Answer & Explanation

Otigh1979

Otigh1979

Beginner2021-12-07Added 17 answers

cos2xdx=12x+14sin2x+C
Differentiate both sides with respect to x
ddx[cos2xdx]=ddx[12x+14sin2x+C]
cos2x=ddx[12x]+14ddx[sin2x]+ddx[C]
cos2x=12+14[2cos2x]+0
cos2x=1+cos2x2
Note that the last equation is an identity, which you should know
Hence the formula has been verified as correct
Result:
On differentiation, we get
cos2x=1+cos2x2

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