Definite Integration Question 32

Question 32

  1. If g(x)=0xcos4tdt, then g(x+π) equals

(1997, 2M) (a) g(x)+g(π) (b) g(x)g(π) (c) g(x)g(π) (d) g(x)g(π)

Show Answer

Solution:

  1. Given, g(x)=0xcos4tdt

g(x+π)=0π+xcos4tdt

=0πcos4tdt+ππ+xcos4tdt=I1+I2

where, I1=0πcos4tdt=g(π)

and I2=ππ+xcos4tdt

Put t=π+y

dt=dy

I2=0xcos4(y+π)dy

=0x(cosy)4dy=0xcos4ydy=g(x)

g(x+π)=g(π)+g(x)



NCERT Chapter Video Solution

Dual Pane