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The number of solution of the equation i...

The number of solution of the equation `int_(-2)^(x)|cos x|dx=0,0ltxlt(pi)/(2)`, is

A

0

B

1

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
`int_(-2)^(x)|cosx|dx=int_(-2)^(-pi//2)|cos x|dx+int_(-pi//2)^(x)|cos x|dx`
`" "=int_(-2)^(-pi//2)-cosxdx+int_(-pi//2)^(x)cosxdx`
`" "1-sin 2+sinx+1`
`therefore" "int_(-2)^(x)|cos x|dx=0`
`rArr" "-1sin2+sinx+1=0`
`rArr" "sinx=sin2-2lt-1`
`therefore" No solution in "(0,(pi)/(2)).`
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