Find L[f(t)] if&nbsp;f(x)={t2,0&lt;t&lt;2t−1,2&lt;t&lt;37,t&gt;3

To find L[f(t)], we need to use the Laplace transform of f(t), which is defined as:ℒ[f(t)](s)=∫0∞e−stf(t)dtLet's evaluate the Laplace transform of f(t) piecewise:For 0&lt;t&lt;2:ℒ[f(t)](s)=∫02e−stt2dt=2s3(s2−2s+2)For 2&lt;t&lt;3:ℒ[f(t)](s)=∫23e−st(t−1)dt=e−2ss2−e−3ss2−e−3ssFor t&gt;3:ℒ[f(t)](s)=∫3∞e−st(7)dt=7e−3ssTherefore, the Laplace transform of f(t) is given by:ℒ[f(t)](s)={2s3(s2−2s+2)0&lt;t&lt;2e−2ss2−e−3ss2−e−3ss2&lt;t&lt;37e−3sst&gt;3Therefore, we have found the Laplace transform of f(t) for the given piecewise function.