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प्रश्न
The value of `int_0^(π/4) (sin 2x)dx` is ______.
विकल्प
0
1
`1/2`
`-1/2`
उत्तर
The value of `int_0^(π/4) (sin 2x)dx` is `underlinebb(1/2)`.
Explanation:
`int_0^(π/4) (sin 2x)dx`
Let u = 2x
If x = 0 then, u = 0
and x = `π/4` then u = `π/2`.
`\implies` du = 2 dx
`1/2 int_0^(π/2) sin u du = -1/2 [cos u]_0^(π/2)`
= `-1/2 [0 - 1]`
= `1/2`
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