Evaluate the following integral: `int_0^pi5(5-4costheta)^(1//4)sinthetad theta`

Explanation

Given,I=`int_0^pi5(5-4costheta)^(1//4)sinthetad theta`

Put,`5-4costheta= x`

`⇒ sin(θ) dθ = dx/4`

When `theta = 0, x =1`,

When ` theta= π, x=9`

I=`int_0^9 5x^(1//4)(dx/4)`

I=`5/4int_0^9 x^(1//4)(dx)`

I=`[x^(5/4)]_1^9`

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