`int_0^(1/2) cos^(-1) x dx` Evaluate the integral

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Let's first evaluate the indefinite integral by using the method of integration by parts,




Now let's evaluate `intx/sqrt(1-x^2)dx` using the method of substitution,

Let's substitute `t=1-x^2`







substitute back `t=1-x^2`



Now let's evaluate the definite integral,






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