Question

Integration of ∫ cos x dx (upper limit-π/2, lower limit-0) is

Answer 1

Step-by-step explanation:

I=∫

0

π/2

∣sinx−cosx∣dx

First look at the graph of sinx & cotx

Both the curve sinx & cosx are positive in I

st

quadrant.

I=∫

0

π/2

(sinx−cosx)dx

=∫

0

π/2

sinxdx−∫

0

π/2

cosxdx

=−[cosx]

0

π/2

−[sinx]

0

π/2

=−[cos

2

π

−cos0]−[sin

2

π

−sin0]

=−[0−1]−[1−0]

=1−1=0.

solution