Mathematics

# For $x\neq 2$ , if $\int_{4-x}^x e^x(4-x)dx=2$, then $\int_{4-x}^x xe^{(4-x)}dx$ is equal to

2

##### SOLUTION

$\\\int_{4-x}^{x} e^x(4-x)dx=2\\let x=4-t\\then dx=-dt\\and if x=x, t=4-x\\if x=4-x, t=x\\\therefore\>I=\int_{x}^{4-x}e^{4-t}t(-dt)\\=\int_{4-x}^{x}e^{4-t}t dt=2\\replace \>t \>by x\\I=\int_{4-x}^{x}e^{4-x}x dx=2$

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One Word Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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