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Question
Solve the following problem.
Evaluate the following integral: \[\int_0^{\frac{\pi}{2}}\] sin x dx
Solution
Using \[\int_{a}^{b}\] f(x) dx = F(x)`|_"a"^"b"`
∴ \[\int_0^{\frac{\pi}{2}}\] sin x dx = - cos x `|_0^(pi//2)`
`= - [cos (pi/2) - cos 0]`
Since,
`cos (pi/2) = 0 and cos 0 = 1`
\[\int_0^{\frac{\pi}{2}}\] sin x dx = - (0 - 1) = 1
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