shamieh
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Evaluate the following integrals.
a) $\int^1_0 x e^x dx$
So integrating by parts we get
$u = x $ $vu = e^x dx$
$du = dx$ $ v = e^x$
$uv - \int vdu = x e^x - \int^1_0 e^x dx$
$$xe^x - e^x |^1_0 = 1$$
b) $$\int^1_0 x^2 e^x \, dx$$
Integrating by parts we get
$$u = x^2 $$ $$ dv = e^x dx$$
$$du = 2xdx$$ $$ v = e^x$$
$$uv - \int vdu = x^2 e^x - \int^1_0 e^x 2x = e^1 - 2 $$
a) $\int^1_0 x e^x dx$
So integrating by parts we get
$u = x $ $vu = e^x dx$
$du = dx$ $ v = e^x$
$uv - \int vdu = x e^x - \int^1_0 e^x dx$
$$xe^x - e^x |^1_0 = 1$$
b) $$\int^1_0 x^2 e^x \, dx$$
Integrating by parts we get
$$u = x^2 $$ $$ dv = e^x dx$$
$$du = 2xdx$$ $$ v = e^x$$
$$uv - \int vdu = x^2 e^x - \int^1_0 e^x 2x = e^1 - 2 $$
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