Mathematics

$$\overset { 1 }{ \underset { 0 }{ \int }  } xe^x dx=$$


ANSWER

$$1$$


SOLUTION
$$I=\overset { 1 }{ \underset { 0 }{ \int }  } xe^xdx..............(1)$$
$$\int xe^x=xe^x-\int1.e^xdx$$
            $$=xe^x-e^x$$
            $$=e^x(x-1)$$
From (1)
$$I=\overset { 1 }{ \underset { 0 }{ \int }  } xe^xd^x-[e^x(x-1){ ] }_{ 0 }^{ 1 }$$
$$=e(1-1)-e^0(0-1)$$
$$=e\times0-1(-1)$$
$$=0+1$$
$$I=1$$
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Single Correct Medium Published on 17th 09, 2020
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