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प्रश्न
Evaluate the definite integral:
`int_0^(pi/4) (2 sec^2 x + x^3 + 2) dx`
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उत्तर
Let `I int_0^(pi/4) (2 sec^2 x+ x^3 + 2) dx`
`[2 tan x x^4/4 + 2x]_0^(pi/4)`
`= 2 (tan pi/4 - tan0) + 1/4 (pi^4/256 - 0) + 2 (pi/4 - 0)`
`= 2 (1 - 0) + pi^4/1024 + pi/2`
`= pi^4/1024 + pi/2 + 2`
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