1.

Integrate (√x - sinx/2 cosx/2+5) dx​

Answer»

Answer:

D = C - 1/2

Step-by-step explanation:

All answers show you a METHOD by

using sin(2x) = 2sin(x)COS(x)

However, you can also SOLVE it by using substitution and the property that d(sin(x)) = cos(x) dx.

Substitute sin(x/2) = t.

Hence, d(t) = 1/2*cos(x/2)d(x)

Therefore, the integral becomes easier i.e.,

Int of 2*t*d(t)

Int. 2*t*d(t) = t^2 +C = (sin(x/2)) ^2 +C

Since, cos(x) = 1 - 2*(sin(x/2)^2)

And “C” can be written as any constant, i will just take the value of half from it

(sin(x/2)) ^2 +C = 1/2 - cos(x) /2 + D, where D = C - 1/2

Remember, when using substitution, also update the limits.

I hope helps to you


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