What is the integral from pi to 2pi of 4sin^2(t)+2t ?

The integral from pi to 2pi of 4sin^2(t)+2t is 2pi+3pi^2

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integral from pi to 2pi of 4sin^2(t)+2t

\int_{π}^{2 π} 4 sin^{2} (t) + 2 t d t

2 π + 3 π^{2}

Decimal Notation

35.89199 \dots

Solution steps

\int_{π}^{2 π} 4 sin^{2} (t) + 2 t d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{π}^{2 π} 4 sin^{2} (t) d t + \int_{π}^{2 π} 2 t d t

\int_{π}^{2 π} 4 sin^{2} (t) d t = 2 π

\int_{π}^{2 π} 2 t d t = 3 π^{2}

= 2 π + 3 π^{2}

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What is the integral from pi to 2pi of 4sin^2(t)+2t ?
The integral from pi to 2pi of 4sin^2(t)+2t is 2pi+3pi^2