Answer
$\dfrac{3}{2}$
Work Step by Step
Re-arrange the given integral as follows:
$\int_{0}^{1}[\dfrac{1}{2}xy^2e^x]_{1}^{2} dx=\int_{0}^{1}[\dfrac{3}{2}xe^x] dx$
or, $[\dfrac{3}{2}xe^x-\dfrac{3}{2}e^x]_{0}^{1} =\dfrac{3}{2}(1)e^{1}-\dfrac{3}{2}e^{1}-\dfrac{3}{2}(1)(0)+\dfrac{3}{2}(1)$
This implies that
$\dfrac{3}{2}-0=\dfrac{3}{2}$
