The area (in sq. units) bounded by curves y=cosec x,y=secx,y=cosx and y=sinx on interval (0,π2) is equal to
A
1+ln(√2+1)
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B
2ln(√2+1)
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C
2ln(√2+1)−√2
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D
ln(√2+1)−1√2
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Solution
The correct option is C2ln(√2+1)−√2
Area =π/4∫0(secx−cosx)dx+π/2∫π/4(cosec x−sinx)dx =π/4∫0secxdx−π/4∫0cosxdx+π/2∫π/4cosec xdx−π/2∫π/4sinxdx =ln(√2+1)−1√2−ln(√2−1)−1√2 =2ln(√2+1)−√2