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First we observe that:\$\\simplify[std]{int ({t}*exp({b}/{c}*x)+{1-t}*ln({b}x+{c}),x)={t*c}/{b}*exp({b}/{c}*x)+({1-t}/{b}*({b}x+{c})*(ln({b}x+{c})-1))+C}.\$

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Hence we have:

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\$\\begin{eqnarray*} \\simplify[std]{defint ({t}*exp({b}/{c}*x)+{1-t}*ln({b}x+{c}),x,{b1},{b2})}&=&\\left[\\simplify[std]{{t*c}/{b}*exp({b}/{c}*x)+({1-t}/{b}*({b}x+{c})*(ln({b}x+{c})-1))}\\right]_{\\var{b1}}^{\\var{b2}}\\\\&=&\\var{ans}\\end{eqnarray*}\$

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to 3 decimal places.

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Enter the area $A$ here to 3 decimal places:

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", "

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5

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Find the area $A$ of the shape bounded by the $x$-axis, the function $y=\\simplify[std]{{t}*exp({b}/{c}*x)+{1-t}*ln({b}x+{c})}$ and the lines $x=\\var{b1},\\;x=\\var{b2}$.

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Finding areas under graphs using definite integration.

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rebelmaths

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