$\int_0^1\left(\ln\left(1+x\right)\right)dx$
$\int_1^exlnx\:dx$
$\int_1^2x\ln\left(x\right)dx$
$\int_0^3\sqrt{9-x^2}dx$
$\int_0^{\infty}\left(xe^{-x}\right)dx$
$\int_{-\infty}^0\left(xe^x\right)dx$
$\int_{-\infty}^0xe^xdx$
Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b
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