T=2

$i(t)=10t \hspace{2cm} when 0 \lt t \leq1 \\ i(t)=0 \hspace{2.4cm}when 1 \leq t \leq 2 \\ I_{rms}=\sqrt{\dfrac 12 \int\limits^2_0i^2dt} \\ I^2_{rms}=\dfrac 12 \int\limits^2_0i^2dt \\ =\dfrac 12 \bigg[\int\limits^2_0i^2dt+\int\limits^2_0i^2dt\bigg] \\ \dfrac 12=\bigg[100\bigg[\dfrac{t^3}{3}\bigg]^1_0+0\bigg] \\ =\dfrac 12 \times100 \times \dfrac 13 \\ I_{rms}=\sqrt{\dfrac{100}{2\times3}} \\ I_{rms}=\sqrt{\dfrac{50}{3}} \\ I_{rms}=4.0825 A$