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Question
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to ______.
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Solution
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to e – 1.
Explanation:
Let I = `int_0^(pi/2) cos x "e"^(sinx) "d"x`
Put sin x = t
⇒ cos x "d"x` = dt
∴ I = `int_0^1 "e"^"t" "dt"`
= `["e"^"t"]_0^1`
= `"e"^1 - "e"^0`
= e – 1
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