integration

g(x) = âˆ« cos⁴t dt , then g(x+Ï€ ) = ? { lower limit =0 upper limit= x}
a. g(x) + g(Ï€)
b. g(x) - g(Ï€)
c.g(x) *g(Ï€)
d. g(x)/g(Ï€)

1 Answers

106

Asish Mahapatra ·2009-07-30 03:18:01

g(x) = _o^xâˆ«cos⁴tdt
= (1/4)*âˆ«(1+cos2t)²dt
= (1/4)âˆ«1+2cos2t + (1+cos4t)/2 dt
= (1/4) [3t/2+sin2t+(sin4t)/8]^x_o
= (1/4) [3x/2+sin2x+(sin4x)/8]

So g(x+Ï€) = (1/4)[3x/2+sin2x+(sin4x)/8 + 3Ï€/2]
= g(x)+g(Ï€)

hence (a)

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